Preheat the oven to 350℉. Spray a 9x5-inch loaf pan with nonstick spray, and then dust with flour (or use baking spray).
MAKE THE BANANA BREAD BATTER:
In a large bowl, whisk together the flour, baking soda and salt.
In a separate large bowl, whisk together the sugar, butter, buttermilk, vanilla, egg and egg yolk until smooth. Pour the wet ingredients over the dry and stir until combined. Stir in the mashed bananas.
MAKE THE CHEESECAKE FILLING:
In a small bowl, stir together the cream cheese, egg, flour and sugar.
ASSEMBLE and BAKE:
Pour half of the banana bread batter into the prepared pan. Then add spoonfuls of the cheesecake filling on top and smooth it into an even layer. Top with the remaining banana bread batter.
Bake for about 1 hour, until the bread is golden, and a toothpick inserted into the center comes out clean. Let cool before removing from the pan and slicing.