Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a medium bowl, whisk together 1 1/2 cups flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine mashed bananas, granulated sugar, egg, melted butter, and vanilla extract. Mix until smooth.
Add the dry ingredients to the banana mixture and stir just until combined.
Fold in the sour cream gently until the batter is uniform.
In a small bowl, prepare the streusel topping by mixing 1/2 cup brown sugar, 1/3 cup flour, and ground cinnamon.
Cut in the cold cubed butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Spoon the batter evenly into the muffin cups, filling each about 3/4 full.
Sprinkle the streusel topping evenly over each muffin.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and allow them to cool in the tin for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.