Heat a skillet over medium-low heat and add the thinly sliced ham. Cook for 1-2 minutes until the ham is lightly browned and heated through. Remove from the skillet and set aside.
Place one slice of Texas toast on a cutting board. Layer the cheddar cheese and warm ham evenly over the bread, then top with the second slice of bread.
Spread about 1 tablespoon of mayonnaise on the outside of each slice of bread.
Place the sandwich in the same skillet over medium heat. Cook for 3-4 minutes per side, pressing gently with a spatula, until the bread is golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve immediately while the cheese is hot and melty.
