Put the dry ingredients (flours, cornmeal, baking powder, baking soda, and salt) in the large bowl and stir until combined.
Crack the eggs into the small bowl and beat with the fork or whisk until the yolk and white are pale yellow. Be sure to wash your hands with soap and water after handling raw eggs!
Add the remaining wet ingredients (buttermilk, milk, and 2 tablespoons oil or butter) to the small bowl, and mix well.
Add the wet ingredients to the dry ingredients and mix until just combined. The batter will be lumpy; do not keep mixing until it is perfectly smooth because this will make your pancakes tough. If the batter seems too thick, add another cup of milk (thinner batter will make thinner pancakes; thicker batter will make thicker ones).
Put the skillet on the stove and turn the heat to medium. When the skillet is hot, add the remaining 1 tablespoon oil or butter.
Drop ladlefuls of batter onto the skillet and cook until there are tiny bubbles on the edges of each pancake’s surface. Using the spatula, flip the pancakes over and cook until golden, about 2 minutes. Serve right away, drizzled with maple syrup or topped with a spoonful of jam.