Put 2 slices of bread on a cutting board or work surface. Top each with 1 slice of the Cheddar, 2 slices of bacon, a slice of Monterey Jack cheese, the remaining slice of Cheddar and another slice of bread; press down lightly.
Heat 1 tablespoon of the butter in a large skillet over medium-low heat. Add the sandwiches and cook until the bread toasts and the cheese is slightly melted, 3 to 5 minutes. Turn with a spatula and add the remaining 1 tablespoon butter to the pan. Cook until the second side is toasted and the cheese is melted, about 3 minutes more, adjusting the heat as needed to keep the bread from burning before the cheese melts.?
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