Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
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 combined.
Add the dry ingredients to the wet ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
In a small bowl, prepare the crumble topping by mixing brown sugar, 1/3 cup flour, and ground cinnamon.
Cut the cold cubed butter into the crumble mixture using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Sprinkle the crumble topping 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 allow them to cool in the tin for 5 minutes before transferring to a wire rack to cool completely.