Preheat the oven to 350°F (175°C) and line a 9x5-inch loaf pan with parchment paper, greasing the sides lightly.

Mash the ripe bananas in a large mixing bowl until mostly smooth.

Mix melted butter, brown sugar, granulated sugar, mashed bananas, egg, and vanilla extract together until fully combined.

Fold in the all-purpose flour, baking soda, cinnamon, and salt gently until no dry streaks remain.

Beat the softened cream cheese in a separate bowl until completely smooth, then mix in sugar, egg, sour cream, and vanilla until creamy.

Spread half of the banana bread batter into the prepared loaf pan, spoon the cheesecake mixture on top, then add remaining banana bread batter.

Bake for 55-65 minutes until the edges are set and the center has a slight wobble.

Cool the cheesecake at room temperature for about 30 minutes, then refrigerate for at least 4 hours before slicing.