Place the 2 slices of bread on a cutting board; spread 1 side of each slice with a tablespoon of butter.
Heat a dry small nonstick skillet over medium heat.
Place 1 slice of bread, butter side down, in the pan and top with cheddar cheese, deli ham (fold and layer each piece), and then the Swiss cheese.
Arrange the second slice of bread, butter side up, on top.
Cook the sandwich until golden brown underneath, about 2 minutes. Carefully flip the sandwich using a flat spatula. Gently press down on the sandwich with that spatula to encourage even browning and help the cheese melt.
Cook until the second side is golden brown and the cheese is melted, about 2 minutes.
Once golden brown on both sides and the cheese has melted, remove from the heat and serve.