Combine whole wheat flour, brown sugar, baking powder, cinnamon, baking soda, salt, ginger, and nutmeg in a mixing bowl, ideally one with a lip for pouring the batter later. Mix with a fork or whisk.
Combine milk, eggs, banana, oil, and vanilla extract in another bowl. Beat together using a hand mixer until frothy.
Heat a griddle or frying pan to 350 to 375 degrees F (175 to 190 degrees C), depending on altitude.
Pour milk mixture over the flour mixture and mix until just combined and most lumps have incorporated into the batter. Fold in apple. Let batter rest for 5 minutes.
Pour or ladle 1/3 cup of batter onto the griddle. Cook until edges are dry and bubbles form on the edges, 2 to 3 minutes. Flip and cook until bottom is golden brown, about 2 minutes more. Repeat with remaining batter.
