Mix grated Fontina and Muenster in a bowl. Spread Dijon thinly over the inner faces of 2 bread slices.
Divide half the grated mixture over those slices, add provolone and then the remaining grated cheese. Close with the other bread slices.
Spread mayonnaise thinly over the outer faces. Heat a large skillet over medium-low heat for 2 minutes.
Cook sandwiches for 4 minutes on the first side until golden. Turn, cover for 2 minutes to help the center melt, then uncover and cook for 2 to 3 minutes more until the second sides are crisp.
Rest for 1 minute, cut each sandwich in half and serve while all three cheeses are soft.