Mix Cheddar cheese, horseradish mustard, garlic, salt, pepper, and cayenne pepper together in a bowl.
Spread 1 teaspoon butter on one side of a slice of bread. Flip; spread Cheddar cheese mixture evenly over unbuttered side. Top with the other slice of bread. Spread 1 teaspoon butter on top.
Preheat a griddle over medium-high heat. Place sandwich on the griddle and press down with a spatula to flatten slightly. Cook until browned, 2 to 3 minutes. Flip and continue cooking until second side is browned, 2 to 3 minutes more.
