Preheat the oven: Preheat the oven to 350°F (175°C). Wrap the outside of an 11-inch (28 cm) springform pan tightly with two or three layers of heavy-duty aluminum foil.
Prepare the crust: Combine the cookie crumbs, granulated sugar, and melted butter in a bowl. Stir until the crumbs are evenly moistened.
Bake the crust: Transfer the mixture to the springform pan and press it firmly and evenly across the bottom using the base of a glass. Bake for 10 minutes, then remove it from the oven and allow it to cool slightly. Keep the oven on.
Prepare the filling: Place the softened cream cheese, granulated sugar, sour cream, and vanilla extract in a large bowl. Mix on low speed just until smooth and combined. Do not overmix.
Add the eggs: Add the eggs one at a time, mixing briefly on low speed after each addition.
Add the cornstarch: Add the cornstarch and mix only until incorporated. Scrape the sides and bottom of the bowl as needed.
Assemble the cheesecake: Pour the filling over the slightly cooled crust and smooth the top with a spatula.
Prepare the water bath: Place the wrapped springform pan inside a large roasting pan. Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan.
Bake the cheesecake: Bake for 60 minutes. The edges should be set, but the center should still wobble slightly when the pan is gently moved.
Let it rest: Carefully remove the cheesecake from the water bath and allow it to rest for 15 minutes. Keep the oven turned on.
Prepare the sour cream topping: Mix the sour cream, granulated sugar, and vanilla extract until smooth. Carefully spoon the mixture over the warm cheesecake and spread it evenly.
Bake the topping: Return the cheesecake to the oven and bake for another 10 minutes.
Cool and chill: Remove the cheesecake from the oven and allow it to cool completely at room temperature. Cover and refrigerate overnight.
Prepare the mixed berry topping: Add the mixed berries, sugar, gelatin-based cake glaze, and water to a small saucepan. Cook over medium heat, stirring continuously, until the mixture comes to a boil and thickens.
Add the berry topping: Remove the berry mixture from the heat and carefully spread it over the chilled cheesecake.
Chill before serving: Refrigerate the finished cheesecake for at least 30 minutes, or until the berry topping is completely set. Remove it from the springform pan, slice, and serve well chilled.