In a large mixing bowl, combine the all-purpose flour, sugar, baking powder, and salt. Whisk these ingredients together until they are well mixed.
In another bowl, beat the egg and then add the milk, buttermilk, melted butter, mashed bananas, and vanilla extract. Mix well until the ingredients are fully incorporated.
Pour the wet ingredients into the bowl of dry ingredients. Gently fold the mixture together using a spatula or wooden spoon. Be careful not to overmix; some lumps are okay!
Heat your griddle or frying pan over medium heat. If you're using a non-stick surface, you may not need to add any extra oil, but if you're unsure, feel free to lightly grease it with some butter.
Once the griddle is hot, pour about 1/4 cup of batter for each pancake onto the surface. Cook until bubbles form on the surface and the edges look set, about 2-3 minutes. Flip the pancakes and cook for another 1-2 minutes until golden brown.
Remove the pancakes from the griddle and serve immediately. Top with your favorite syrup, fresh fruit, or a sprinkle of nuts for extra texture. Enjoy your warm, fluffy banana pancakes!