Add the banana, milk, melted butter, and vanilla to a medium bowl.
Add the flour, sugar, baking powder, and salt and stir to make an even and thick batter.
Heat a nonstick skillet or griddle over medium-low heat. Add a sliver of butter (or oil) and swirl to coat the pan.
Add 1/4 cup batter and cook for 3-4 minutes per side, flipping when you see bubbles around the edges. Repeat to make the rest of the batch. (To make mini pancakes, use 1 tablespoon batter.)
Serve warm with desired toppings.
Notes
Store leftovers in an airtight container in the refrigerator for up to 5 days or for 6 months in the freezer. Pop into the toaster to warm through.
Use dairy milk or soy milk, almond milk, mixed nut milk, or any other nondairy milk you prefer.
Serve with maple syrup, applesauce, any fruit puree, or yogurt as you like.