Preheat a non-stick skillet or grill pan over medium heat with a splash of olive oil until shimmering, about 2 minutes.

In a large mixing bowl, combine shredded cooked chicken, mozzarella, cheddar cheese, cream cheese, minced garlic, parsley, salt, and pepper. Blend everything together thoroughly.

Lay out tortillas and evenly distribute the cheesy chicken mixture onto each, then roll tightly around the filling.

Carefully place the seam-side down wraps into the hot skillet. Cook for 2-3 minutes until golden brown and crispy. Flip and cook for another 2-3 minutes.

Remove from the pan, let cool for a minute, then slice each wrap in half and serve immediately.