In a mixing bowl, combine shredded chicken, softened cream cheese, shredded mozzarella, minced garlic, and olive oil. Season with salt and pepper and stir until evenly mixed and creamy.

Lay each tortilla flat on a clean surface. Spoon an even portion of the chicken mixture down the center of each tortilla, leaving room at the edges.

Tightly roll each tortilla, tucking in the ends as you go to keep the filling secure. Press the seam to seal.

Heat a skillet over medium heat. Place the wraps seam-side down in the skillet and cook for 3 to 4 minutes per side, or until the tortilla is golden brown and crisp and the cheese is melted inside.

Transfer the wraps to a cutting board. Let rest for 1 minute, then slice each in half on a diagonal. Sprinkle with chopped parsley if using and serve immediately.