Preheat a skillet or grill pan over medium heat and add olive oil. While heating, warm your tortillas for 10-15 seconds in the microwave covered with a damp paper towel to prevent cracking.
In a mixing bowl, combine the shredded chicken, mozzarella cheese, cheddar cheese, softened cream cheese, minced garlic, parsley, salt, and pepper. If using spinach, add it at this stage. Mix thoroughly until the cream cheese coats everything evenly.
Divide the chicken mixture evenly among the four low-carb tortillas, placing about ½ cup in the center of each. Roll each tortilla tightly, tucking in the sides as you go to form secure wraps.
Place the wraps seam-side down in the preheated skillet. Cook for 2-3 minutes per side without moving them, until the wraps are golden brown and the cheese is melted and slightly oozing from the edges.
Remove from skillet, slice each wrap in half diagonally, and serve hot. Garnish with extra parsley if desired.
