Follow these steps carefully for perfect mini eclairs. The process is divided into making the cream first (as it needs to chill), then the pastry, and finally, assembling your beautiful creations.

Part 1: Prepare the Vanilla Pastry Cream

It is essential to make the pastry cream first, as it needs several hours to chill and set completely before it can be piped into the eclair shells.

1. Heat the Milk: Split the vanilla bean lengthwise and scrape the seeds into a medium saucepan. Add the pod and the milk. Bring the milk to a gentle simmer over medium heat. Once you see bubbles forming around the edges, remove it from the heat and let it steep for about 15 minutes to infuse the vanilla flavor. After steeping, remove the vanilla pod.
2. Prepare the Egg Yolk Mixture: In a separate medium-sized heatproof bowl, whisk together the granulated sugar, cornstarch, and salt until well combined. Add the egg yolks and whisk vigorously until the mixture is pale yellow, thick, and smooth. This process is called blanching the yolks and helps ensure a smooth final product.
3. Temper the Eggs: This is a critical step to prevent the eggs from scrambling. While whisking the egg yolk mixture continuously, slowly pour about half of the hot milk into the bowl in a thin, steady stream. This gently raises the temperature of the eggs.
4. Cook the Cream: Pour the tempered egg mixture back into the saucepan with the remaining milk. Return the saucepan to the stove over medium heat. Whisk constantly and vigorously, making sure to scrape the bottom and corners of the pan to prevent scorching.
5. Thicken the Cream: The mixture will begin to thicken. Continue cooking and whisking for 1-2 minutes after it begins to bubble. It should be very thick, similar to the consistency of pudding.
6. Finish and Chill: Remove the saucepan from the heat. Immediately stir in the cold butter until it is fully melted and incorporated. Strain the pastry cream through a fine-mesh sieve into a clean, shallow bowl. This guarantees a perfectly silky-smooth texture by removing any small cooked egg bits.
7. Cover and Chill: Press a piece of plastic wrap directly onto the surface of the cream. This prevents a skin from forming. Refrigerate for at least 4 hours, or preferably overnight, until completely cold and firm.

Part 2: Prepare the Choux Pastry Shells

The magic of choux pastry happens when the water in the dough turns to steam in the hot oven, causing the shells to puff up dramatically.

1. Preheat and Prepare: Preheat your oven to 400°F (200°C). Line two baking sheets with parchment paper. Do not grease the sheets, as this can cause the eclairs to spread too much.
2. Combine Liquids: In a medium saucepan, combine the water, milk, cubed butter, sugar, and salt. Place over medium-high heat and bring the mixture to a rolling boil.
3. Add the Flour: As soon as it boils, remove the pan from the heat and add all the flour at once. Stir vigorously with a wooden spoon or heatproof spatula until the flour is completely incorporated and a thick paste forms.
4. Cook the Dough: Return the saucepan to medium heat. Continue to cook the dough, stirring and mashing it against the sides of the pan for about 2-3 minutes. The goal is to cook out some of the excess moisture. The dough is ready when it pulls away cleanly from the sides of the pan and a thin film forms on the bottom.
5. Cool the Dough: Transfer the hot dough to the bowl of a stand mixer fitted with the paddle attachment (or a large bowl if using a hand mixer). Beat the dough on low speed for 2-3 minutes to allow some of the steam to escape and cool it down slightly. The dough should be just warm to the touch, not hot, before adding the eggs.
6. Incorporate the Eggs: With the mixer on low-medium speed, add the room temperature eggs one at a time. It is crucial that you wait for each egg to be fully and completely incorporated before adding the next. The dough may look separated or curdled at first, but keep mixing, and it will come back together into a smooth, glossy paste.
7. Check for Consistency: After adding all four eggs, the final paste should be thick, smooth, and glossy. To check for the correct consistency, lift the beater. The dough that falls off should form a distinct “V” shape or a slow-forming ribbon that hangs without breaking immediately. If the dough is too stiff, you can add a fifth egg that has been whisked, adding it a little at a time until the right consistency is reached.
8. Pipe the Eclairs: Transfer the choux paste to a large piping bag fitted with a large round or open star tip (about 1/2-inch or 1.5 cm). Pipe 2.5 to 3-inch long logs onto the prepared baking sheets, leaving about 2 inches of space between each one to allow for expansion. Use a wet finger to gently pat down any small points on the ends of the piped dough.
9. Bake to Perfection: Place the baking sheets in the preheated oven. Bake at 400°F (200°C) for 15 minutes. Then, without opening the oven door, reduce the temperature to 350°F (175°C) and bake for another 15-20 minutes.
10. Dry the Shells: The eclairs are done when they are a deep golden brown, feel light, and sound hollow when tapped. A common mistake is underbaking, which leads to collapse. To ensure they are crisp, turn off the oven, prop the door open slightly with a wooden spoon, and let the shells dry out in the cooling oven for 15-20 minutes.
11. Cool Completely: Transfer the baked eclair shells to a wire rack to cool completely before filling.

Part 3: Prepare the Chocolate Glaze and Assemble

This is the final, rewarding step where all the components come together.

1. Make the Glaze: Place the finely chopped chocolate in a medium heatproof bowl. In a small saucepan, heat the heavy cream and corn syrup until it just begins to simmer around the edges.
2. Melt the Chocolate: Pour the hot cream mixture over the chopped chocolate. Let it sit, undisturbed, for 5 minutes to allow the heat to gently melt the chocolate.
3. Stir to Smoothness: Starting from the center and working your way out, gently stir the mixture until the chocolate is completely melted and the ganache is smooth and glossy. Stir in the softened tablespoon of butter until fully incorporated.
4. Cool the Glaze: Let the glaze cool for 10-15 minutes at room temperature. It should be slightly thickened but still fluid and pourable. You want it to be warm, not hot.
5. Fill the Eclairs: Give your chilled pastry cream a good whisk to loosen it up and make it smooth again. Transfer it to a piping bag fitted with a small round filling tip. To fill the eclairs, poke three small holes in the bottom of each cooled shell (one at each end and one in the middle). Pipe the pastry cream into the holes until the eclair feels heavy and full. Wipe away any excess cream.
6. Glaze the Eclairs: Hold each filled eclair by its sides and carefully dip the top surface into the warm chocolate glaze. Lift it up and let any excess glaze drip off. You can tilt the eclair slightly to help the glaze coat evenly.
7. Set and Serve: Place the glazed eclairs on a wire rack or back on the parchment-lined baking sheet. Allow the glaze to set at room temperature for about 30 minutes, or refrigerate for 10-15 minutes if you’re in a hurry. Eclairs are best served the day they are made.