In a bowl, combine the flour, baking powder, salt and sugar and mix well with a whisk.
In a large bowl, combine the egg, peanut butter, and milk and beat with an electric mixer.
Add the 3 tablespoons of melted butter, then add the flour mixture all at once and beat until extremely smooth, about 2 to 3 minutes. Stir in one-fourth of the banana slices.
Grease a griddle or a frying pan with the remaining 1 teaspoon of butter and heat over medium heat.
Using a ladle or measuring cup, pour about ¼ cup of batter for each flapjack, leaving about 2 inches between them. When the top surface is bubbling, the edges opaque, and the bottom side golden brown, after about 1½ minutes, use a spatula to flip each flapjack. Cook until the other side is golden brown, about 45 seconds to 1 minute. Repeat until all the batter is used.
Serve stacks of flapjacks with bananas, peanuts or honey.