Set out the eggs and milk so that they can warm to room temperature while you prepare the other ingredients (this will prevent the butter from hardening when mixing it into the eggs and milk)
Set the skillet on the stove and turn on the burner for a minute just to warm the skillet. Make sure it doesn't get hot or you will end up burning the butter. Once the skillet is warm, turn the burner off and then place the butter in the skillet so that it melts while you prepare the other ingredients.
Add the flour, cornmeal, sugar, baking powder and salt to a bowl and mix them together well. Create a well in center of the dry mixture and set it aside.
In a separate bowl, add the eggs, milk and melted butter and then mix well with a whisk. After pouring the butter from the skillet, grease the entire skillet by using a paper towel to rub the left over butter up the inside edges of the skillet. Set the skillet aside.
Pour the wet mixture into the dry ingredients and then mix everything together well. Now, pour the mixture back into the buttered skillet.
Place the skillet in the oven and bake for 20-25 minutes.