First, take the cream cheese and eggs out of the fridge so they come to room temperature.
Next, you'll make the blueberry sauce because it needs time to chill.
In a small pan: add all of the blueberry sauce ingredients to the pan except the vanilla extract. Stir to combine. Bring to a boil, stirring constantly, then reduce heat to a simmer.
Simmer for about 10 minutes, until it thickens and reduces slightly. Remove from heat and stir in the vanilla extract.
Transfer to a heat-proof bowl and allow to chill to room temperature.
Preheat oven to 325℉. Line an 8x8 pan with parchment paper.
Crush the graham crackers and pour the graham cracker crumbs into a large bowl. Mix in the white and brown sugar, then pour melted butter and mix until evenly distributed.
Press graham cracker mixture into an 8x8 pan. Bake for 8 minutes at 325℉, then remove and let cool.
Beat the room-temperature cream cheese in a stand mixer until it turns creamier, about 4-5 minutes.
Add in the remaining ingredients (sugar, eggs, egg white, vanilla extract, and flour). Beat until smooth, about 1-3 minutes.
Pour the cheesecake filling over the cooled crust. Gently tap it on the counter to remove any visible air bubbles.
Using a spoon, pour drops of blueberry sauce into the filling and swirl the sauce around to distribute it.
Bake the bars for 35-50 minutes - until the internal temperature is 150℉.
Once they are done, let them sit on the counter to cool for an hour, then transfer to the fridge for at least 6 hours, but overnight is better.
Store in the fridge.
