Preheat the oven to 375 degrees Fahrenheit. Prepare a muffin pan with cupcake liners and set aside.
Ina large mixing bowl, mash the bananas with a fork or masher. Add the egg, butter, and vanilla extract and stir until the egg is well combined. Then stir in the granulated sugar and brown sugar. Set aside.
In a separate mixing bowl, combine the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Add the flour mixture to the egg mixture and combine (a thick, sticky dough will form, soft enough to drip off the spoon but thick enough to hold its shape).
Mix in the chopped nuts. (optional)
Scoop about ¼ cup of dough into each baking cup of the prepared muffin pan (each should be nearly full, slightly more than ¾ full).
Bake for 16-19 minutes, or until the muffins are slightly browned around the edges and the tops hold their shape when gently pressed with your finger.
Carefully transfer to a cooling rack and allow to cool slightly before serving.