Blend the banana, eggs, vanilla, oil, and milk in a blender until just combined. Alternatively you could just hand mash the banana then whisk in the other wet ingredients, but you won't get as the smooth consistency of a blender.
In a medium bowl, whisk the flour, baking powder, and salt. Slowly stir in the wet ingredients and mix until just combined.
I find the pancakes turn out best when the batter sits for at least 5 minutes. Then scoop about 1/4 cup per pancake into a warm (medium heat) well oiled pan. Cook for a few minutes each side.
To flip the pancakes, gently wedge a spatula under. The spatula should easily nudge under, otherwise leave on another minute.
Add all your favorite toppings and enjoy. Save leftovers for up to five days in the fridge. I don't recommend freezing.