Preheat the oven to 450°F. Grease two standard 12-cup muffin tins or line them with paper liners; silicone muffin molds also work well.

Melt the butter in a medium saucepan over medium heat. Keep cooking, swirling the pan occasionally, until the butter foams, turns a deep golden brown, and smells nutty. Remove from the heat and let it cool slightly.

Mash the bananas in a large bowl. Add the pumpkin puree, browned butter, brown sugar, vanilla, and eggs, then whisk until the mixture is smooth.

Sprinkle the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and pumpkin pie spice over the wet mixture. Fold with a rubber spatula just until no dry streaks remain; be careful not to overmix the batter.

Scoop the batter into the prepared muffin cups, filling each one all the way to the top.

Make the cinnamon sugar topping in a small bowl: stir together the flour, granulated sugar, and cinnamon. Add the softened butter and work it in with a fork until the mixture is crumbly. Sprinkle about 1 teaspoon of the topping over each muffin.

Bake at 450°F for 5 minutes, then reduce the oven temperature to 350°F and bake for 25 more minutes (about 15 minutes for mini muffins), or until a toothpick inserted in the center comes out clean.

Let the muffins cool in the tin for 5 minutes, then transfer them to a wire rack to cool completely. Serve warm with plenty of butter. The recipe makes 24 standard muffins or 48 mini muffins.