Preheat a cast-iron skillet over low heat for about 5 minutes.

Slice two pieces of sourdough bread, each about ½-inch thick.

Grate 3.5 oz of cheddar cheese and 1 oz of gruyère cheese.

Spread 1 teaspoon of mayonnaise evenly on one side of each slice of sourdough.

Melt 1 tablespoon of unsalted butter in the skillet, swirling to coat the surface.

Place one slice of bread, mayonnaise side down, into the skillet; pile the grated cheeses on top, then place the second slice with mayonnaise side up.

Cover the skillet and cook for 2-3 minutes until the bottom slice is golden brown.

Carefully flip the sandwich and cook for an additional 2 minutes until both sides are crisp and golden.

Remove from the skillet, cut in half diagonally, and serve immediately.