Preheat oven to 350°F and line a muffin tin with paper liners.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
In a large bowl, mix mashed bananas, granulated sugar, and brown sugar until smooth.
Add egg, vegetable oil, and vanilla extract. Stir to combine.
Fold in the flour mixture and chopped nuts just until combined. Do not overmix.
Fill muffin liners about three-quarters full with batter.
In a separate bowl, beat cream cheese until smooth. Add sugar, egg yolk, and vanilla extract. Mix well.
If the cream cheese mixture is too thick, add milk to loosen slightly.
Spoon one tablespoon of cream cheese mixture on top of each muffin and swirl lightly with a toothpick.
Bake for 16 to 18 minutes, until a toothpick inserted comes out clean.
Cool in the pan for 5 minutes, then transfer to a wire rack to finish cooling.