In a large mixing bowl, combine the softened cream cheese, shredded mozzarella, shredded cheddar, grated Parmesan, and minced garlic. Mix until well combined. Gently fold in the shredded chicken, chopped parsley, salt, and pepper until the chicken is evenly coated.

Lay a tortilla flat. Spoon a portion of the chicken mixture onto the center, leaving space around the edges. Fold in the sides of the tortilla first, then tightly roll it up from the bottom to create a burrito-style wrap.

Melt butter or heat oil in a large non-stick skillet over medium heat. Place wraps seam-side down in the pan. Cook for 3-4 minutes per side, until the tortilla is golden-brown and crispy, and the cheese is melted. Repeat with the remaining wraps.