Whisk flour, baking powder, sugar, and salt together in a mixing bowl. Combine milk, banana, peanut butter, egg, canola oil, and vanilla extract in a separate bowl; pour into the flour mixture and whisk together until thoroughly mixed.
Ladle batter in 1/4 cup portions onto hot griddle. Cook until tiny air bubbles form on top, 2 to 5 minutes; flip and continue cooking until the bottoms are browned, 2 to 3 minutes. Repeat with remaining batter. Keep finished pancakes warm.