In a small skillet, melt the butter over medium heat. Add minced garlic and sauté for 1–2 minutes until fragrant but not browned. Stir in parsley and remove from heat.
In a large bowl, mix shredded chicken, cream cheese, shredded cheese, garlic powder, salt, and pepper. Pour in half of the garlic butter mixture and stir until everything is well combined.
Lay out the tortillas and divide the chicken mixture evenly among them. Roll each tortilla tightly like a burrito, folding in the sides to secure the filling.
Heat a large skillet or griddle over medium heat. Brush the outside of each wrap with the remaining garlic butter. Place the wraps seam-side down and cook for 2–3 minutes per side until golden brown and the cheese inside is melted.
Slice in half, serve hot, and enjoy with your favorite dipping sauce!