Follow these steps carefully for flawless blueberry lemon cheesecake bars. The key to perfect cheesecake is patience, especially during the mixing and cooling stages.

Step 1: Prepare Your Pan and Oven
Preheat your oven to 325°F (163°C). Line an 8×8 inch square baking pan with parchment paper, leaving an overhang on two opposite sides. This “sling” will make it incredibly easy to lift the entire block of cheesecake bars out of the pan for clean cutting later. Lightly grease the parchment paper and any exposed sides of the pan.

Step 2: Make the Graham Cracker Crust
In a medium bowl, combine the graham cracker crumbs and granulated sugar. Pour in the melted unsalted butter and mix with a fork until all the crumbs are evenly moistened. The texture should resemble wet sand. Pour this mixture into your prepared 8×8 inch pan. Using the bottom of a measuring cup or a flat glass, press the crumbs firmly and evenly into the bottom of the pan to create a compact layer.

Step 3: Pre-Bake the Crust
Place the pan in the preheated oven and bake for 10-12 minutes, or until the edges are lightly golden and the crust is fragrant. This pre-baking step is crucial as it creates a crispier crust that will stand up to the creamy filling and prevent it from becoming soggy. Once baked, remove the pan from the oven and set it on a wire rack to cool completely while you prepare the filling.

Step 4: Create the Blueberry Swirl
While the crust is cooling, prepare the blueberry topping. In a small saucepan, combine the blueberries, granulated sugar, and 1 tablespoon of lemon juice. Cook over medium heat, stirring occasionally, until the blueberries begin to burst and release their juices, about 5-7 minutes. In a small separate bowl, whisk together the cornstarch and cold water until smooth to create a slurry. Pour the slurry into the simmering blueberry mixture, stirring constantly. Continue to cook for another 1-2 minutes, until the sauce has noticeably thickened to a jam-like consistency. Remove from the heat and set aside to cool slightly.

Step 5: Mix the Cheesecake Filling
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the room temperature cream cheese on medium speed until it is completely smooth and creamy, with no lumps remaining. This may take 2-3 minutes. Scrape down the sides and bottom of the bowl frequently to ensure everything is incorporated. Add the granulated sugar and beat on medium-low speed until well combined and smooth. Add the room temperature sour cream and pure vanilla extract, mixing until just combined.

Step 6: Incorporate the Eggs and Lemon
With the mixer on low speed, add the room temperature eggs one at a time, mixing until just combined after each addition. Be very careful not to over-mix once the eggs are in, as this incorporates too much air and can cause the cheesecake to crack during baking. After the eggs are incorporated, turn off the mixer. Add the lemon zest and fresh lemon juice, and gently fold them in with a rubber spatula until just distributed. The final filling should be smooth, thick, and velvety.

Step 7: Assemble and Swirl the Bars
Pour the prepared lemon cheesecake filling over the cooled graham cracker crust and spread it into an even layer with your spatula. Now, take your slightly cooled blueberry sauce and drop spoonfuls of it evenly over the top of the cheesecake filling. Using a butter knife or a wooden skewer, gently drag the tip through the blueberry dollops and the cheesecake filling to create a beautiful marbled or swirled pattern. Don’t overdo it; a few simple passes are all you need for a stunning visual effect.

Step 8: Bake the Cheesecake Bars
Place the pan in the 325°F (163°C) oven and bake for 35-45 minutes. The cheesecake is done when the edges are set and appear slightly puffed, but the center still has a slight jiggle or wobble when you gently shake the pan. It should not be completely liquid, but it should not be firm all the way through either. This residual heat will finish cooking the center as it cools.

Step 9: The Crucial Cooling Process
This is the most important step for preventing cracks and achieving the perfect texture. Do not skip it.

1. Oven Cooling: Turn off the oven, crack the oven door open slightly, and leave the cheesecake inside for 1 hour. This allows it to cool down gradually, preventing temperature shock that leads to cracking.
2. Counter Cooling: After an hour, remove the pan from the oven and place it on a wire rack to cool to room temperature, which will take another 1-2 hours.
3. Refrigeration: Once it has reached room temperature, cover the pan loosely with plastic wrap and transfer it to the refrigerator to chill for at least 4 hours, but preferably overnight. This final chill is essential for the cheesecake to set up completely, allowing for clean cuts and the development of its full flavor.

Step 10: Cut and Serve
Once fully chilled, use the parchment paper overhangs to lift the entire block of cheesecake out of the pan and onto a cutting board. For the cleanest possible slices, use a large, sharp knife. Dip the knife in hot water and wipe it clean between each cut. Cut into 16 small squares and serve chilled.