Combine flour, sugar, baking powder and salt in a bowl and stir to combine well. Set aside.
In a separate bowl, combine egg, milk, buttermilk, melted (cooled) butter, mashed banana and vanilla extract. Mix until well combined, but do not over mix.
Combine dry ingredients with wet ingredients and mix until all the dry ingredients are well combined, but do not overmix. The batter SHOULD be lumpy. Let batter sit for at least three minutes, allowing it to slightly bubble up. Do not stir at this point, or it will destroy the air bubbles that help make pancakes fluffy.
Brush a non-stick griddle or frying pan with a light coating of butter or oil, then heat to medium heat. Make sure pan is heated prior to adding batter to it. Scoop batter onto the pan, approximately 1/4 cup for each pancake. Cook until pancake begins to puff up, bubbles appear in batter and the sides of the pancake appear to have cooked, then flip and cook the second side until golden brown. Serve immediately.