Make garlic butter: Melt 1 tablespoon butter in a small skillet over medium heat. Add minced garlic and cook for 1 minute until fragrant but not browned. Remove from heat and set aside.
Prepare filling: In a medium bowl, combine softened cream cheese and sour cream, stirring until smooth. Add half the mozzarella cheese, garlic powder, Italian seasoning, salt, and pepper. Fold in shredded chicken until evenly coated.
Assemble wraps: Lay each tortilla flat. Spoon a quarter of the chicken mixture down the center. Sprinkle with remaining mozzarella and cheddar cheese. Fold short ends toward center, then roll tightly from one side. Place seam-side down.
Cook wraps: Heat remaining 1 tablespoon butter in a large skillet over medium heat. Brush each wrap with prepared garlic butter. Place seam-side down in skillet and cook for 3 minutes per side until golden brown and cheese is melted, pressing gently with a spatula.
Serve: Slice wraps diagonally in half. Garnish with fresh parsley if desired. Serve immediately while hot and crispy.
