Preheat a large skillet or grill pan over medium heat and add the olive oil.

Warm the tortillas in the microwave for 10 to 15 seconds, covered with a damp paper towel, until soft and flexible.

In a medium mixing bowl, combine the shredded chicken, mozzarella, cheddar, cream cheese, minced garlic, parsley, salt, pepper, and spinach if using, and mix until the cream cheese evenly coats the filling.

Divide the chicken mixture into 4 equal portions and place each portion in the center of a tortilla.

Roll each tortilla tightly around the filling, folding in the sides as you roll to form secure wraps.

Place the wraps seam side down in the preheated skillet and cook for 2 to 3 minutes without moving, until the bottoms are golden brown.

Flip the wraps and cook for another 2 to 3 minutes, until the second side is golden and the cheese is melted.

Transfer the wraps to a cutting board, rest for 1 to 2 minutes, then slice each wrap in half diagonally and serve hot.