Combine chicken, mozzarella, cheddar, and Parmesan in a large bowl.
Add 120 g of filling to each tortilla, fold in sides, and roll tightly.
Stir melted butter, garlic, and parsley in a small bowl.
Brush wraps with garlic butter and cook seam-side down in a skillet over medium heat for 2–3 minutes per side.
Preheat oven to 190°C. Brush wraps again, place on a lined baking sheet, and bake for 10–12 minutes, flipping once.
Serve hot with ranch, marinara, or garlic aioli.