In a non-stick pan, over medium-low heat,melt 1/2 Tbsp. butter, swirling the pan to evenly coat. Sprinkle 2 Tbsp. cheddar in the shape of your toast with the hole cut out. Add the bread on top and grill on medium-low until the cheese is crispy and golden.
Remove the toast from the pan, melt the other half of the butter and swirl to coat. Arrange the remaining cheese in the shape of the bread and place your toast in the pan, cheeseless side down and crispy cheese side up.
Crack the egg into the hole and cook on medium-low, covered with a glass lid, until the egg is done to your liking. Add salt and pepper if desired.