Butter each slice of bread on one side.
Heat large frying pan and place bread butter-side down in the pan, frying until golden brown.
Remove bread from the pan and make 2 sandwiches with the cheese with the browned side on the inside.
Butter the 4 sides of the bread and with a 2" round cutter, cut a ring out of the middle of each sandwich. Keep the circle of bread still in the sandwich.
Heat the frying pan and pop in the whole sandwiches.
Fry on 1 side until browned and crisp.
Remove the middles and turn everything over.
Crack one egg into each hole.
The lids will be a good indicator of how quickly the undersides of the bread is cooking.
Continue frying the sandwiches gently until the egg is cooked to your liking.
Remove from the pan and top with the 'hat'.