Preheat oven to 375°F (190°C). Line a 12-cup muffin tin with liners or grease with butter.
In a large bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Set aside.
In another bowl, mash bananas until mostly smooth. Add egg, vanilla extract, and sugar. Whisk until well combined.
Stir in melted butter and sour cream until just combined.
In a small bowl, mix together brown sugar, flour, cinnamon, and salt for the crumb topping. Cut in cold butter with fingers or pastry cutter until mixture resembles coarse crumbs.
Add the banana mixture to the dry ingredients. Gently fold together with a spatula until just combined. Do not overmix.
Divide batter evenly into muffin cups, filling about ¾ full. Top generously with crumb topping.
Bake for 18–22 minutes, or until a toothpick comes out with a few moist crumbs. Muffin tops should spring back when touched.
Cool in pan for 5 minutes, then transfer to a wire rack.