Heat a skillet or grill pan over medium heat and drizzle in the olive oil.
While the pan warms, place the tortillas in the microwave covered with a damp paper towel and heat for 10 to 15 seconds to soften and prevent cracking.
In a large bowl, stir together the shredded chicken, mozzarella, cheddar, cream cheese, garlic, parsley, salt, and pepper; fold in the spinach if using, ensuring everything is well coated.
Spoon about half a cup of the chicken mixture onto the center of each tortilla and roll them up tightly, folding in the edges to secure the filling.
Arrange the wraps seam-side down in the skillet and cook them without moving for around 2 to 3 minutes per side until golden brown and the cheese inside is melted.
Remove from the heat, cut each wrap diagonally in half, and serve immediately with extra parsley sprinkled on top if you like.
