Combine the strawberries, blueberries, and raspberries in a blender or food processor. Puree until smooth. Press through a fine-mesh sieve into a medium saucepan and discard the pulp.

Whisk in the sugar and cornstarch and cook over medium heat until very thick and jammy, about 10-15 minutes. Set aside to cool to room temperature.

Line a 9-inch springform pan with parchment paper.

Combine the graham cracker crumbs and melted butter in a medium bowl. Stir to fully coat the crumbs in the butter. Press tightly into the bottom and 1 inch up the sides of the prepared pan. Freeze while you make the filling.

In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl using a handheld electric mixer, beat the cream cheese, sugar, vanilla, and salt together on medium speed until smooth and creamy.

In a separate medium bowl, beat the cold heavy cream on medium-high speed until stiff peaks form.

Add the berry jam to the filling. Continue to mix until well incorporated.

Using a silicone spatula, gently fold the whipped cream into the cheesecake mixture until fully combined.

Spread the filling into the prepared crust. Use an offset spatula to smooth the surface.

Cover and refrigerate for 6-8 hours or overnight until fully chilled and set.

Just before serving, garnish with berries and whipped cream if desired.