The trick to crisping the cheese properly is to use a gentle, medium-low flame the entire time.

Melt 3/4 of the butter in a large non-stick skillet over medium-low flame, coating pan thoroughly

Place the bread side-by-side in the skillet

Cover one slice evenly with half of the grated cheese (about 1/4 cup)

Top the cheese with the other slice of bread, with the butter side up

Sprinkle the buttered top evenly with about 2 tablespoons of the remaining grated cheese

Melt the remaining butter in the pan alongside the sandwich

Flip the sandwich immediately so the cheese-covered top is now facing down in the butter

Sprinkle remaining cheese on top of sandwich

Cook sandwich gently until the cheese on bottom is crisp and golden, about 3-4 minutes

Flip sandwich and cook until cheese on the second side is golden-crisp, another 3-4 minutes

Eat and enjoy immediately!