Mash the ripe banana in a bowl until smooth.
In a separate bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, combine the milk, egg, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Fold in the mashed banana gently into the batter.
Heat a non-stick skillet over medium heat and lightly grease it with butter.
Pour 1/4 cup of batter onto the skillet for each pancake.
Cook until bubbles form on the surface, about 2-3 minutes.
Flip the pancakes and cook for another 1-2 minutes until golden brown.
Remove from skillet and keep warm while cooking remaining pancakes.