In a small bowl, combine the flour, baking powder, and salt. Set aside.
In a large bowl, mash the banana with a fork until it's smooth, puree-like. See the note below. To the mashed banana, add the egg, milk, melted butter, and vanilla extract. Whisk the egg thoroughly while mixing it with the other liquid ingredients, and mix until everything is combined.
Add the dry ingredients to the banana mixture, and mix from the outside of the bowl in, until there's no visible flour left. Some of the lumps are the mashed banana, those are ok. Add the finely chopped walnuts to the bowl and fold them into the batter with just a few turns.
Cook the pancakes:
Heat a non-stick griddle or large pan over medium-high heat. Once hot, grease, spray, or melt butter on the hot surface. When using an electric griddle, heat it somewhere between 300 and 350F. Immediately, pour ¼ cup of pancake batter onto the greased pan.
Cook the pancakes for about 2 minutes, until the edges begin to look defined and bubbles form. Flip the pancakes over and cook for another minute on the other side. Avoid pressing down on the pancake after flipping; this will make the pancakes dense and chewy with undercooked batter on the sides from oozing out. Remove the pancakes from the pan onto a plate and keep them warm, either on a plate covered with a kitchen towel or in the oven set to 200F on a sheet pan, while you cook the rest of the batter.
Serve & store:
Plate a couple of these banana nut pancakes, top with your favorite toppings and syrups.
Leftover pancakes will keep in the fridge for up to 3 days in an airtight container, or freeze them flat, then transfer them into a zip bag where they'll last up to 3 months. Reheat them in the microwave for 30 seconds to 1 minute or in a toaster.
Notes
For an added touch, add 1 teaspoon of ground cinnamon to the dry ingredients.
Since pancake batter naturally has a mild, neutral flavor, it's important to use aluminum-free baking powder. This ingredient often leaves a salty/metallic aftertaste in pancakes.