In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt until well combined.
In a separate bowl, mash the ripe banana until smooth. Add the egg, milk, melted butter, and vanilla extract to the mashed banana, and whisk until combined.
Pour the wet ingredients into the bowl of dry ingredients. Use a spatula or wooden spoon to gently fold the mixture together until just combined. Do not overmix; a few lumps are fine.
Heat a non-stick skillet or griddle over medium heat. Add a small amount of butter or oil to grease the surface.
Pour about 1/4 cup of batter onto the hot skillet for each pancake. Use the back of a spoon or a spatula to spread the batter into a round shape, if needed. Cook until bubbles form on the surface of the pancakes and the edges begin to set, about 2-3 minutes.
Carefully flip the pancakes with a spatula and cook for an additional 1-2 minutes on the other side, or until golden brown and cooked through.
Transfer the cooked pancakes to a plate and keep warm while you cook the remaining batter. Serve the pancakes warm with your favorite toppings, such as sliced bananas, maple syrup, honey, or chopped nuts.
Serve these fluffy banana pancakes for breakfast or brunch, and enjoy the delicious, comforting flavor of ripe bananas in every bite!