In a medium bowl, whisk together the egg, buttermilk, butter, banana, and sugar.
In a separate bowl, sift together the flour, baking powder, baking soda, salt, and nutmeg.
Pour the liquid ingredients over the dry ingredients and stir together with a fork or small whisk just to combine (overstirring makes the pancakes tough). It is okay if the batter is a little bit lumpy.
Heat a nonstick griddle or skillet over medium-high heat. Brush the pan lightly with oil and drop the batter onto the heated skillet in mounded ¼-cup portions.
Cook the pancakes until the batter starts to brown around the edges and little bubbles start to form over the surface of the batter, 1 to 2 minutes. Use your spatula to lift a corner of the pancake to see if it is brown and lacy and ready to turn. Flip the pancake and finish cooking, 1 to 2 minutes longer. Repeat with the remaining pancake batter, brushing the pan with more oil when needed to prevent sticking.
Serve the warm pancakes drizzled with melted butter, sliced bananas, fresh strawberries, warmed Nutella, and/or Buttery Brown Sugar Syrup.