Melt the butter in a medium saucepan over medium heat. Once fully melted and foaming, add the minced garlic and sauté for about 1 minute, stirring constantly until fragrant but not browned.

Pour in the heavy cream and add the Italian seasoning, salt, and black pepper. Whisk everything together and bring the mixture to a gentle simmer. Let it cook for 3 to 5 minutes, stirring occasionally, until the sauce begins to thicken slightly.

Reduce heat to low and gradually stir in the grated Parmesan cheese, whisking constantly until completely melted and the sauce is smooth and creamy. Remove from heat and set aside.

In a large bowl, combine the shredded chicken with about half of the prepared Alfredo sauce and 1 cup of the shredded mozzarella cheese. Mix until the chicken is thoroughly coated.

Lay a tortilla flat on your work surface. Spoon a generous portion of the chicken mixture into the center, leaving about 2 inches around the edges. Fold in the left and right sides toward the center, then roll up tightly from the bottom. Repeat with remaining tortillas.

Heat a large non-stick skillet or griddle over medium heat. Place the wraps seam-side down in the skillet, working in batches if necessary. Cook for 2 to 3 minutes on the first side until golden brown and crispy. Flip carefully and cook for another 2 to 3 minutes on the second side.

Transfer the toasted wraps to serving plates. Drizzle the remaining Alfredo sauce over the top or serve on the side. Sprinkle with the remaining mozzarella cheese and chopped fresh parsley. Optional: place under the broiler for 1 to 2 minutes to melt the cheese on top.