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 mashed bananas, granulated sugar, beaten egg, melted butter, vanilla extract, and sour cream. Mix until well combined.
Add the dry ingredients to the wet ingredients and gently fold until just combined. Do not overmix.
In a small bowl, prepare the crumble topping by mixing 1/2 cup flour, brown sugar, and ground cinnamon. Add cold cubed butter and use your fingers or a pastry cutter to blend until the mixture resembles coarse crumbs.
Divide the muffin batter evenly among the 12 muffin cups, filling each about 3/4 full.
Sprinkle the crumble 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 muffins from the oven and allow them to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.