Preheat the oven to 300°F and line an 8-inch square baking dish with parchment paper.

To make the crust, mix together the graham cracker crumbs, brown sugar, and melted butter in a bowl. Spread the mixture evenly in the prepared baking dish and refrigerate.

Using a hand mixer or a stand mixer with a paddle attachment, beat the cream cheese until smooth. Add the sweetened condensed milk, sour cream, and vanilla extract and continue mixing until well combined, scraping the sides of the bowl as needed. Finally, mix in the mashed banana, even if there are some lumps in the filling.

Pour the filling into the crust and bake for 40 minutes or until the filling is firm and golden in color. Allow the cheesecake to cool completely before refrigerating it for at least 4 hours.

Slice and serve.