Preheat your oven to 325°F (165°C).

In a mixing bowl, combine the crushed graham crackers, ½ cup of sugar, and melted butter. Stir until the mixture resembles wet sand.

Firmly press this mixture into the base of a 9-inch springform pan to create an even crust. Bake for 10 minutes, then allow it to cool completely.

In a large bowl, whip the softened cream cheese with 1 cup of sugar and the vanilla extract until silky and smooth.

Incorporate the eggs one at a time, ensuring each is fully blended before adding the next.

In another bowl, puree the assorted berries with the cornstarch and lemon juice until smooth.

Spread half of the cream cheese mixture over the cooled crust. Spoon dollops of the berry puree on top, then layer the remaining cream cheese mixture over it.

Using a knife or a skewer, gently swirl the berry puree into the cheesecake to create a marbled design.

Place the cheesecake in the preheated oven and bake for 55-60 minutes, or until the center is set but still has a slight wobble.

Once done, turn off the oven and let the cheesecake cool inside for an hour.

After cooling, let the cheesecake reach room temperature, then chill it in the refrigerator for a minimum of 4 hours, or ideally overnight, before slicing and serving.