For the cake:

1. Preheat oven to 350° and butter and flour a 9×5 loaf pan. Set aside.
2. In a large bowl, whisk together flour, baking soda, and salt.
3. In another large bowl, combine sugar, melted butter, buttermilk, vanilla, 1 egg and egg yolk and mashed bananas. Mix until smooth.
4. Pour wet ingredients over dry and stir until combined.

For the filling:

1. In a small bowl, using a hand mixer, mix together the egg, cream cheese, flour, vanilla and sugar until completely combined.
2. Pour half of the batter into the prepared pan.
3. Dollop the cream cheese filling on top and smooth in an even layer with a spatula. Top with remaining batter.
4. Bake until golden and a toothpick comes out clean, approximately 1 hour.
5. Let cool at least 10 minutes before slicing and serving.