Preheat your oven to 325°F (160°C).
Prepare the crust by mixing graham cracker crumbs, sugar, and melted butter in a bowl.
Tightly pack the crust mixture into the bottom of a 9-inch springform pan.
Bake the crust in the preheated oven for about 10 minutes.
In a large mixing bowl, beat softened cream cheese and sugar until smooth and creamy.
Add sour cream, vanilla extract, and mix until well-combined.
Add eggs one at a time, mixing gently to avoid over-beating.
Fold in the mashed bananas and strawberry puree gently until just combined.
Pour the filling over the pre-baked crust, smoothing the top with a spatula.
Bake the cheesecake in the oven for 55 to 60 minutes, or until the edges are set and the center is slightly wobbly.
Turn off the oven and let the cheesecake cool with the oven door ajar for about an hour.
Refrigerate the cheesecake for at least 4 hours before serving, ideally overnight.