Preheat a greased griddle over medium heat.
In a mixing bowl, mash the banana into a puree, or leave a little bit of chunkiness.
Crack in the eggs and beat together with the mashed banana.
For added fluffiness, you could also add 1/2 teaspoon baking powder at this time.
Stir in the walnuts and vanilla extract.
Pour about a 1/4 cup onto hot griddle.
Cook until edges are dry.
Turn, cook until the other side is browned to your liking.