Preheat your oven to 375°F (190°C).
In a large bowl, combine the shredded chicken, mozzarella cheese, cream cheese, mayonnaise, minced garlic, Italian seasoning, salt, and black pepper. Mix until well combined.
Lay out the flour tortillas on a clean surface. Spread a layer of the chicken mixture evenly over each tortilla, leaving about an inch of space around the edges.
Top the chicken mixture with fresh spinach leaves and diced tomatoes. Sprinkle grated Parmesan cheese on top.
Roll each tortilla tightly, starting from one end and tucking in the sides as you go. Place the wraps seam-side down on a baking sheet lined with parchment paper.
Brush the tops of the wraps lightly with olive oil to help them crisp up in the oven.
Bake in the preheated oven for 15-20 minutes, or until the wraps are golden brown and the cheese is melted.
Remove from the oven and let cool for a few minutes before slicing into halves or quarters. Serve warm.