Preheat the oven to 350°F (175°C). Mash the ripe bananas in a large bowl until you have a chunky puree; small lumps are fine.
Add the sugar, egg, melted butter, and vanilla to the bananas and stir until combined. In a separate bowl, whisk together the flour, baking soda, and salt. Gently fold the dry ingredients into the wet mixture until no flour streaks remain; do not overmix.
For the topping, mix the brown sugar, flour, and cinnamon in a small bowl. Work in the cold cubed butter with your fingers until pea-sized crumbs form. If your hands run warm, chill the bowl for 5 minutes first to help keep the butter cold.
Line a 12-cup muffin tin with paper liners or grease the cups well. Fill each cup halfway with batter. Sprinkle the topping generously over each muffin, pressing lightly so it sticks.
Bake for 20–25 minutes, until the tops are golden and a toothpick inserted comes out with moist crumbs, not wet batter. Cool in the pan for 5 minutes, then transfer to a rack and allow at least 10 minutes of cooling before eating.