Preheat a griddle or panini press to medium heat (about 350 degrees).
In a small bowl, combine the garlic seasoning and softened butter.
Butter one side of each slice of bread.
Add the cheese and pepperoni to an un-buttered side of bread, then top it with another slice of bread - butter facing up.
Place the sandwich on the griddle. Repeat for all other sandwiches.
Cook until the bottom is browned, 2-3 minutes, then flip and cook the other side until browned. (If using an electric panini press, both sides will cook at the same time, so no flipping necessary.)
Cut into thirds and serve immediately with your favorite pizza dipping sauce!