Arrange the bacon in a single layer in a cold skillet. Bring to medium heat and cook until crispy and well-rendered. Transfer to a paper towel-lined plate. Wipe the skillet clean and reduce heat to medium-low.

Mix the mayonnaise and Parmesan cheese together in a small bowl until fully combined. Spread half of the mixture evenly onto one side of each bread slice.

Place the bread mayo-side down in the skillet. Cook for 2 to 3 minutes until lightly golden. Spread the remaining mayo mixture over the tops of the bread slices, then flip so the fresh mayo side faces down.

Top each bread slice evenly with the shredded cheddar and Monterey Jack. Cover with a lid and cook for 3 to 5 minutes until the bread is deep golden and the cheese is fully melted. If the bread browns too fast, lower the heat slightly.

Remove bread from the skillet. Divide the crispy bacon between two slices and press the halves together firmly. Rest for 1 to 2 minutes before cutting.

Slice in half and serve immediately while hot and crispy.