Heat the oven to 350°F (175°C). Grease a 9 x 5-inch loaf pan and line it with parchment paper, leaving paper overhanging the long sides for easy removal.

Beat the softened cream cheese, 1/4 cup sugar, one egg, 1/2 teaspoon vanilla, and 2 tablespoons flour until smooth. Stop mixing as soon as the ingredients are combined.

Whisk the flour, baking soda, and salt together in a separate bowl so the leavening and salt are evenly distributed.

In another bowl, beat the softened butter and 3/4 cup sugar until creamy. Beat in the two eggs and 1 teaspoon vanilla, then mix in the mashed bananas and sour cream.

Add the dry ingredients to the banana mixture and stir just until no dry flour remains. Do not overmix, or the loaf may become dense.

Spread about half of the banana batter in the prepared pan. Spoon the cheesecake mixture over it, keeping the filling slightly away from the edges, then cover with the remaining banana batter and smooth the top.

Bake for 55–70 minutes. If the top browns too quickly, tent the loaf loosely with foil during the remaining baking time.

Test the loaf by inserting a toothpick into the banana-bread portion rather than only the cheesecake center. It is ready when the toothpick comes out clean or with a few moist crumbs.

Cool in the pan for 15–20 minutes, then transfer the loaf to a wire rack and cool completely before slicing. For cleaner layers, chill the cooled loaf for 30–60 minutes before cutting.