Shred the cooked chicken into bite-sized pieces and place in a large mixing bowl.
Add mozzarella cheese, cream cheese, sour cream, minced garlic, Italian seasoning, salt, and black pepper to the chicken. Mix until well combined.
Lay out the tortillas and spread the chicken mixture evenly across each, leaving space around the edges. Add spinach, tomatoes, and Parmesan cheese on top.
Roll the tortillas tightly, folding in the sides. Heat a skillet over medium heat and coat with cooking spray or olive oil. Cook the wraps seam-side down for 3-4 minutes on each side until golden brown and crispy.
Remove from skillet, let cool for a minute, then slice in half and serve warm.