Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, whisk together 1 1/2 cups flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine the mashed bananas, granulated sugar, and egg. Mix until well combined.
Add the melted butter, vanilla extract, and sour cream to the banana mixture. Stir until smooth.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
In a small bowl, prepare the streusel topping by combining brown sugar, 1/3 cup flour, and ground cinnamon.
Cut the cold butter into the streusel mixture using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Spoon the muffin batter evenly into the prepared muffin tin, filling each cup about 3/4 full.
Sprinkle the streusel topping evenly over each muffin.
Bake for 18 to 20 minutes, or until a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.