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 all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine the mashed bananas, granulated sugar, egg, melted butter, and vanilla extract. Mix until smooth.
Add the dry ingredients to the banana mixture and stir until just combined.
Fold in the sour cream gently until incorporated. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
To make the streusel topping, combine the light brown sugar, 1/3 cup all-purpose flour, and ground cinnamon in a small bowl.
Add the cold cubed butter and use your fingers or a pastry cutter to mix until the mixture resembles coarse crumbs.
Sprinkle the streusel evenly over each muffin batter portion.
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 let them cool in the tin for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.