In a mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, beat the egg and then whisk in the milk and melted butter.
Stir the wet ingredients into the dry ingredients until just combined. Fold in the mashed banana.
Heat a griddle or skillet over medium heat and lightly grease it. Pour ¼ cup of batter for each pancake onto the griddle.
Cook until bubbles form on the surface of the pancakes and the edges look set, about 2-3 minutes. Flip and cook until golden brown on the other side, about 2 minutes more.