In a deep dish, combine eggs, half and half, salt and pepper.
Dip the bread slices into the egg mixture on all sides.
In a skillet, heat oil and butter and add the bread slices and pour the remaining egg mixture around the bread slices.
Close the lid and cook on medium heat until eggs are cooked.
Flip the bread slices over and fold the egg mixture onto the bread.
Top one bread slice with cheese and the other with ham and close the sandwich.
Cover with lid and allow the cheese to melt.
Enjoy.
