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 soda, and salt.
In a large bowl, combine mashed bananas, granulated sugar, beaten egg, melted butter, vanilla extract, and sour cream. Mix until well blended.
Add the dry ingredients to the wet ingredients and gently fold together 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.
Cut in the cold cubed butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Divide the muffin batter evenly among the 12 muffin cups.
Sprinkle the crumble topping evenly over each muffin.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and allow them to cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.