Combine corn meal, flour, sugar, baking powder, and salt in a medium bowl and stir with a spoon to blend.
In a larger bowl, beat 2 eggs with a whisk or fork.
Add the milk and beat again.
Before combining the dry and wet ingredients, put oil and butter in the baking sheet and place in oven for 1-2 minutes to heat up. Watch carefully and remove before it smokes. Remove the pan and tilt to coat entire surface with the oil.
Turn oven down to 375°F.
Add the dry ingredients to the wet ingredients and mix with a whisk or fork, just until well blended. Don’t overmix. Add a little extra milk if the batter is too thick. It should pour like pancake batter.
Pour excess oil from the baking sheet into the cornbread mixture and stir.
Pour batter into prepared baking sheet. Bake 20-25 minutes. Cut into 5-inch squares.