In a large bowl, add in the ripe bananas and beat with a hand mixer until mashed.
Add the melted butter and both sugars. Mix with a hand mixer until combined.
Add the eggs, vanilla extract, and sour cream. Beat until incorporated.
In a separate bowl, add the baking soda, baking powder, and flour. Whisk to combine.
Add the dry ingredients to the wet and mix until incorporated.
Pour about 2 cups of batter into each loaf pan.
Add dollops of the cream cheese mixture to cover all of the banana bread batter. Using a light hand, spread it to cover any spots with banana bread batter still showing through.
Add the remaining batter on top of the cream cheese filling. I added it in dollops to cover all of the cream cheese.
Place into the oven and bake for 50-55 minutes, or until done. Place a toothpick into the center of the loaf. If moist crumbs are stuck on the toothpick, it is done. If it comes out with batter, give it an additional few minutes before testing again.
Let the bread cool completely and turn out onto a serving plate. Cut and serve.
Store in an airtight container.