Preheat the oven to 325°F (160°C). Grease the springform pan with cooking spray or line the bottom with parchment paper.
In a mixing bowl, combine the graham cracker crumbs, granulated sugar, and melted butter. Mix until the crumbs are well coated.
Press the graham cracker mixture firmly into the bottom of the prepared springform pan to form the crust. Bake in the preheated oven for 10 minutes, then remove and let cool.
In a separate bowl, use an electric mixer to beat the softened cream cheese until smooth and creamy. Gradually add the granulated sugar while mixing.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract, sour cream, and heavy cream until the mixture is smooth.
Pour the cheesecake filling over the cooled crust in the springform pan.
Bake in the oven for 40 minutes, or until the edges are set but the center is slightly jiggly. Turn off the oven and let the cheesecake cool in the oven for 1 hour with the door slightly ajar.
After cooling, refrigerate the cheesecake for at least 4 hours or overnight for best results.
For the berry topping, combine the mixed berries, granulated sugar, and lemon juice in a saucepan. Heat over medium heat until the berries begin to release their juices, about 5-7 minutes. Remove from heat and let cool.
Once the cheesecake is chilled, carefully remove it from the springform pan. Top with the cooked berries before serving.