Follow these detailed instructions carefully, and you’ll be rewarded with the most incredible homemade Apple Pie Cinnamon Rolls. We’ll break the process down into manageable stages.

Stage 1: Activating the Yeast and Making the Dough

1. Warm the Milk: In a small saucepan or a microwave-safe bowl, gently warm the milk until it is lukewarm, about 105-115°F (40-46°C). It should feel like a warm bath, not hot. If it’s too hot, it will kill the yeast.
2. Activate the Yeast: Pour the warm milk into the bowl of a stand mixer. Sprinkle the active dry yeast and one tablespoon of the granulated sugar over the milk. Give it a gentle stir and let it sit for 5-10 minutes. The mixture should become foamy or bubbly, which indicates the yeast is alive and active.
3. Combine Wet Ingredients: Once the yeast is foamy, add the melted butter, the remaining granulated sugar, and the 2 large eggs to the bowl. Use the whisk attachment to mix everything together until well combined.
4. Add Dry Ingredients: Switch to the dough hook attachment. Add 4 ½ cups of the all-purpose flour and the salt to the wet ingredients.
5. Knead the Dough: Start the mixer on a low speed and mix until the flour is incorporated. Then, increase the speed to medium and let the mixer knead the dough for 7-10 minutes. The dough should become smooth, elastic, and pull away from the sides of the bowl. If the dough is excessively sticky after a few minutes of kneading, add the remaining ½ cup of flour, one tablespoon at a time, until it is manageable. The final dough should be soft and slightly tacky to the touch, but not stick to your fingers.
6. First Rise: Lightly grease a large bowl with oil or cooking spray. Form the kneaded dough into a smooth ball and place it in the greased bowl, turning it over once to coat the top. Cover the bowl with plastic wrap or a clean kitchen towel. Place it in a warm, draft-free spot and let it rise for 1 to 1.5 hours, or until it has doubled in size.

Stage 2: Preparing the Apple Pie Filling

1. Sauté the Apples: While the dough is rising, you can prepare the filling. In a medium saucepan, melt the ¼ cup of butter over medium heat. Add the diced apples and cook, stirring occasionally, for 5-7 minutes, until the apples have softened slightly.
2. Create the Sauce: In a small bowl, whisk together the brown sugar, 2 tablespoons of flour, ground cinnamon, and ground nutmeg.
3. Thicken the Filling: Sprinkle the brown sugar mixture over the softened apples in the saucepan. Stir continuously until the sugar dissolves and the mixture begins to thicken, which should take about 2-3 minutes.
4. Finish and Cool: Remove the saucepan from the heat and stir in the lemon juice. Transfer the apple pie filling to a separate bowl and allow it to cool completely to room temperature. This is a crucial step; a warm filling will melt the dough and make assembly difficult.

Stage 3: Assembling and Shaping the Rolls

1. Roll out the Dough: Once the dough has doubled in size, gently punch it down to release the air. Transfer the dough to a lightly floured surface. Use a rolling pin to roll the dough out into a large rectangle, approximately 18×12 inches in size and about ¼-inch thick.
2. Spread the Filling: Using a spatula, spread the cooled apple pie filling evenly over the surface of the dough, leaving a small ½-inch border along one of the long edges.
3. Roll It Up: Starting from the long edge opposite the clean border, tightly roll the dough up into a log. The clean border will help seal the log shut. Pinch the seam firmly to seal.
4. Slice the Rolls: Using a sharp serrated knife or, for the cleanest cuts, a piece of unflavored dental floss, slice the log into 12 equal-sized rolls, each about 1.5 inches thick.
5. Arrange for the Second Rise: Grease a 9×13-inch baking pan or a large cast-iron skillet with butter or cooking spray. Carefully place the sliced rolls, cut-side up, into the prepared pan. They should be snug but have a little room to expand.
6. Second Rise: Cover the pan loosely with plastic wrap and let the rolls rise in a warm place for another 30-45 minutes, or until they look puffy and have filled most of the gaps in the pan. While they rise, preheat your oven to 375°F (190°C).

Stage 4: Baking and Frosting

1. Egg Wash (Optional): For a beautiful, golden-brown finish, whisk the remaining egg with a tablespoon of milk. Gently brush this egg wash over the tops of the risen rolls.
2. Bake: Place the pan in the preheated oven and bake for 25-30 minutes, or until the rolls are a deep golden brown and the filling is bubbly. If they start to brown too quickly, you can loosely tent the pan with aluminum foil for the last 10 minutes of baking.
3. Make the Frosting: While the rolls are baking, prepare the cream cheese frosting. In a medium bowl, using an electric hand mixer or a stand mixer with the paddle attachment, beat the softened cream cheese and softened butter together on medium speed until smooth and creamy.
4. Finish the Frosting: Reduce the mixer speed to low and gradually add the sifted powdered sugar. Once incorporated, add the vanilla extract. Increase the speed to medium-high and beat for 2-3 minutes until the frosting is light and fluffy. If the frosting is too thick, add milk or cream, one tablespoon at a time, until you reach your desired consistency.
5. Frost and Serve: Once the rolls are done baking, remove them from the oven and let them cool in the pan for 10-15 minutes. It’s best to frost them while they are still warm, but not piping hot. Spread the glorious cream cheese frosting generously over the tops of the warm rolls, allowing it to melt slightly into all the nooks and crannies. Serve immediately.