Preheat oven to 350F. Grease a 9 by 5 loaf pan with melted butter.
In a medium size bowl, mix all cream cheese filling ingredients using a hand mixer. Set aside.
In a large bowl, mix together egg, sugar, oil, Greek yogurt, and vanilla extract. Add bananas to the mixture. Using a hand mixer, mix all ingredients together until well incorporated.
In a small bowl, add flour, baking powder, baking soda, and salt. Use a whisk and mix the ingredients together.
Using a wooden spatula, gently incorporate the dry ingredients to the large bowl that has the banana mixture. Stir until well incorporated. Don't over mix.
Put 2/3 of the banana bread mixture into the loaf pan. Shake gently until leveled. Pour filling mixture slowly to cover the banana bread mixture. Then, pour the rest of the banana bread mixture slowly over the filling mixture. Make it as even as you can.
Bake for 55 minutes, until top is golden. To test for readiness, jiggle the loaf pan to make sure the mixture doesn't jiggle too much. Keep in mind that the cream cheese filling layer will remain pretty soft.
Cool bread for 10-15 minutes before turning out on a rack.