Preheat oven to 350°F (175°C). Grease and flour a loaf pan or square baking dish.
In a small bowl, combine flour, brown sugar, and cinnamon for the crumb topping. Cut in cold butter until crumbly, then set aside.
Whisk together flour, baking powder, baking soda, and salt in a medium bowl.
Beat softened butter and sugar in a large bowl until light and fluffy. Add eggs one at a time, mixing well after each. Stir in vanilla extract.
Mix in mashed bananas. If desired, add sour cream or yogurt for extra moisture.
Gradually add dry ingredients to the wet mixture, mixing just until combined. Pour batter into prepared pan and smooth the surface.
Evenly sprinkle crumb topping over the batter.
Bake for 45 to 55 minutes until a toothpick inserted in the center comes out clean.
Cool cake in the pan for 10 to 15 minutes, then transfer to a wire rack. Slice and serve.