Prepare the Chicken: Start by melting a tablespoon of butter in a skillet over medium heat. Add the minced garlic and sauté until fragrant, taking care not to burn it, which should take about a minute.
Stir in the Alfredo sauce along with shredded chicken, mozzarella, and Parmesan. Sprinkle some salt and pepper to taste. Let it cook for 2-3 minutes until the chicken is heated through and the cheese is melted and gooey.
Assemble the Wraps: Lay each flour tortilla out on a flat surface. Spoon the chicken Alfredo mixture into the center of each tortilla, ensuring you divide the filling evenly among the four tortillas.
Roll and Cook: Carefully fold the sides of each tortilla over the filling, then roll them up tightly to enclose the filling. Heat a skillet over medium-high heat. Place each wrap seam-side down and cook for 2-3 minutes on each side until they are golden and crispy.
Serve: Slice each wrap in half and arrange them on a serving platter. Garnish with a sprinkle of fresh parsley if desired and serve immediately while they're hot.