Preheat the oven to 350˚F (180˚C).
In a medium bowl, mash the bananas. Add the beaten egg, brown sugar, granulated sugar, melted butter, vanilla extract, and Greek yogurt. Mix until well combined.
Add the flour, salt, and baking soda to the banana mixture and stir until just combined.
In a small bowl, prepare the cream cheese filling by mixing the egg, softened cream cheese, sugar, and flour until smooth.
Pour half of the banana bread batter into a greased 9×5-inch (23×12 cm) bread pan.
Evenly spread the cream cheese filling over the banana bread batter. Top with the remaining banana bread batter.
Bake for about 50 minutes, or until a toothpick inserted into the center comes out clean.
Allow the banana bread to cool for 15 minutes before slicing and serving. Enjoy!