Place the bread slices on a cutting board. Spread a thin layer of mayo on one side of each slice.
Flip one slice of bread and spread Dijon mustard on the other side.
Layer the grated cheddar and Gruyère or Raclette cheeses on top of the mustard. Place the other slice of bread on top of the cheese, with the mayo side facing out.
Heat a nonstick or cast-iron skillet over medium-low heat. Melt enough butter in the pan to coat the bottom.
Place the sandwich in the pan, cover, and cook for 2 to 3 minutes, or until the bottom slice of bread is golden brown and crisp.
Flip the sandwich, replace the lid, and cook for another 1 to 3 minutes, until the other side is golden brown and the cheese is melted. Reduce the heat to low if the bread browns too quickly before the cheese melts.
Slice and serve immediately.