1. Place cheese in freezer until well chilled, about 10 minutes. Meanwhile, place bacon on a griddle over medium-high heat; cook until crisp. Transfer to a paper towel-lined plate to drain.

2. Remove cheese from freezer, cut two slices, and grate remaining cheese on the largest holes of a box grater; set aside.

3. Place English muffin split-side down in skillet; cook until toasted. Turn and top each half with a slice of cheese. Reduce heat and cook until cheese is melted. Remove from heat and set aside.

4. Melt butter on griddle; crack egg onto melted and fry until whites are set; turn and top egg with grated cheese; continue cooking until yolk has reached desired degree of doneness.

5. Carefully transfer egg to large muffin half. Top egg with bacon and sandwich with remaining muffin half; serve immediately.