Preheat the oven to 350°F (175°C). Grease and flour a 9-inch square baking pan.
In a medium bowl, whisk together 1 1/2 cups flour, baking powder, baking soda, salt, and 1/2 teaspoon cinnamon. Set aside.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Mix in the mashed bananas and sour cream until just combined.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
To make the streusel topping, combine 1/2 cup flour, brown sugar, and 1 teaspoon cinnamon in a small bowl.
Cut in the cold butter pieces using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Pour the batter into the prepared pan and spread it evenly.
Sprinkle the streusel topping evenly over the batter.
Bake for 45 to 50 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let cool in the pan on a wire rack for at least 20 minutes before slicing and serving.