Shortcut Cornbread with Caramelized Vidalia Onion Fans

1/4 cup vegetable oil or melted butter, plus 2 tablespoons vegetable oil for greasing skillet 

1 small to medium Vidalia onion (or other sweet onion) 

2 large eggs 

1 1/4 cups milk whole  

1/4 cup butter melted 

2 cups white or yellow self-rising cornmeal mix