Heat a non-stick or cast iron skillet on low.
Spread a generous amount of mayonnaise on each slice of bread, making sure to spread to the edges.
Lay the first slice of bread, mayonnaise side down, in the skillet. Add the cheeses on top and then add the remaining bread (mayonnaise side up). The mayo will be on the outside of the sandwich.
Heat gently until the bread is crisp and golden brown (about 5-6 minutes). Flip and cook until the other side is also golden brown (this side usually takes a bit less time).
Serve hot while the cheese is still melty.