Preheat the oven to 350°F (175°C) and grease a 9-inch pan.
In a bowl, mash bananas until smooth.
Cream butter and sugar in another bowl until fluffy. Add eggs and vanilla, mixing well.
Combine flour, baking powder, baking soda, and salt in a separate bowl.
Add dry ingredients to the wet mixture, alternating with sour cream, until combined.
Pour batter into the prepared pan, smoothing the top.
For the streusel, mix brown sugar, flour, cinnamon, and butter until crumbly. Sprinkle over the batter.
Bake for 35 minutes or until a toothpick inserted comes out clean.
Cool slightly, slice, and serve warm.