In a bowl, mix shredded chicken, mayonnaise, Dijon mustard, salt, and pepper until well combined.
Spread the mixture evenly on one slice of garlic bread and sprinkle mozzarella and Parmesan cheese on top.
Place the second slice of garlic bread on top to form a sandwich.
Heat a skillet over medium heat and lightly butter the pan.
Cook the sandwich for 3-4 minutes per side, pressing slightly with a spatula, until golden brown and the cheese is melted.
Remove from heat, let it sit for 1 minute, then slice in half.
Enjoy the gooey, cheesy, garlicky goodness!