Mash the banana on a plate with a fork until it's almost a paste. Some tidbits left are ok.
Make the batter:
In a large bowl, combine the flour, baking powder, and salt.
Make a well in the middle and add the egg, milk, melted butter, and vanilla extract. Use a fork to whisk the egg first and once the egg yolk has broken up with the egg white, begin to mix it with the other liquids. Then, start to incorporate and mix the liquid with the dry ingredients in the bowl until you have a smooth batter.
Add the mashed banana and the coconut flakes and gently combine them with the rest of the batter. You only need a few turns to mix them well.
Cook the pancakes:
Heat a non-stick griddle or large pan over medium 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. Remove the pancakes from the pan onto a plate and keep them warm while you cook the rest of the batter.
Serve:
Plate a few pancakes on a plate and top them with your favorite toppings and syrups.
Notes
To ripen your banana in a pinch, peel the banana and microwave it in 15-second intervals, mashing it with a fork as it softens. This will quick-ripen the banana and bring out its sweetness. Then, allow it to cool down completely before making the batter.
Since pancake batter naturally has a mild, neutral flavor, it's important to use aluminum-free baking powder. The metallic flavor will ruin the taste, especially in fluffy pancake recipes that call for 2 or more teaspoons. Trust me on this one.