In a large bowl, mix together flour, baking powder, baking soda, and salt.
In another bowl, mix banana, brown sugar, cinnamon, vanilla, egg, and milk.
Add the banana mixture to the flour mixture and stir until just blended. Add additional milk if the batter looks too thick.
Heat griddle or frying pan over medium. It's ready for cooking when a sprinkle of water bounces off.
Just before cooking, stir melted butter into the batter.
Pour batter by 1/3-cup fulls onto the griddle. Cook until sides are dry and bubbles have formed on top, then flip. Continue cooking until pancakes have puffed and are golden brown. Repeat with remaining batter, adjusting griddle heat as necessary.
Serve with banana slices, maple syrup, or your favorite toppings.