Preheat a skillet or grill pan over medium heat. Add olive oil. While heating, wrap your tortillas in a damp paper towel and microwave for 10-15 seconds to prevent cracking.

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

Place about 1/2 cup of filling in the center of each tortilla. Fold in the sides and roll tightly from the bottom up to form secure wraps. Do not overfill.

Place wraps seam-side down in the hot skillet. Cook for 2-3 minutes per side without moving them, until golden brown and the cheese is melted and slightly oozing from the edges. If browning too quickly, reduce heat to medium-low.

Remove from heat. Slice each wrap in half diagonally. Garnish with extra parsley and serve immediately.