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, egg, melted butter, vanilla extract, and buttermilk. Mix until well blended.
Add the dry ingredients to the wet ingredients and stir 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 the cold cubed butter to the crumble mixture 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.
Sprinkle the crumble topping evenly over each muffin.
Bake for 18 to 20 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 pan for 5 minutes before transferring to a wire rack to cool completely.