Prepare the pan and oven
Preheat the oven to 325°F / 160°C. Line the bottom of a 9-inch springform pan with parchment paper.
Make the crust
Add the biscuits or graham crackers and sugar to a food processor. Pulse until the mixture looks like fine crumbs. Pour in the melted butter and pulse again until evenly moistened.
Press and bake the crust
Press the crumb mixture firmly into the bottom of the pan and slightly up the sides. Use the bottom of a glass or measuring cup to compact it. Bake for 10 minutes, then let it cool while you prepare the toppings and filling.
Prepare the blueberries
In a small bowl, toss the blueberries with sugar and flour. Add the lemon juice and stir until the berries are evenly coated. Set aside.
Make the crumble
In another bowl, mix flour and dark brown sugar. Pour in the melted butter and stir with a fork until small crumbs form. Set aside.
Mix the cheesecake filling
Beat the cream cheese on low speed until smooth. Add the sugar and mix until creamy, scraping down the bowl as needed.
Add sour cream, vanilla, and eggs
In a small bowl, stir the sour cream and cornstarch together until smooth. Add it to the cream cheese mixture with the vanilla. Mix on low speed. Add the eggs two at a time, mixing gently just until combined.
Assemble the cheesecake
Pour the cheesecake filling over the cooled crust. Scatter the blueberry mixture over the top, then sprinkle the crumble evenly over the berries.
Bake in a water bath
Place the springform pan inside a larger cake pan or wrap the outside securely with layers of foil. Set it into a roasting pan and pour hot water around it to create a water bath. Bake for 1 hour 20 minutes to 1 hour 30 minutes, or until the edges are set and the center has a slight wobble.
Cool slowly
Turn off the oven, crack the oven door, and let the cheesecake cool inside for 1 hour. Remove it from the water bath and let it cool to room temperature.
Chill before serving
Refrigerate the cheesecake for at least 6 hours, preferably overnight, before slicing. This helps the filling set cleanly.