Preheat a skillet or grill pan over medium heat and add olive oil. Warm your tortillas in the microwave for about 10-15 seconds, covering them with a damp paper towel to keep them from cracking.

In a mixing bowl, combine shredded chicken, mozzarella cheese, cheddar cheese, softened cream cheese, minced garlic, chopped parsley, salt, and pepper. If adding spinach, toss it in at this stage. Mix thoroughly until the cream cheese covers the entire mixture evenly.

Divide the chicken mixture evenly among the four low-carb tortillas, placing about 1/2 cup of filling in the center of each. Roll each tortilla tightly, tucking in the sides to create secure wraps.

Place the wraps seam-side down in the preheated skillet. Cook for 2-3 minutes per side without moving them, until golden brown and the cheese begins to melt and ooze slightly from the edges.

Remove from the skillet, slice each wrap in half diagonally, and serve hot. Garnish with extra parsley if desired.