Preheat a skillet over medium heat and add olive oil. Let it heat until shimmering, about 2 minutes.

Warm tortillas in the microwave for 10-15 seconds covered with a damp paper towel.

In a mixing bowl, combine chicken, mozzarella, cheddar, cream cheese, garlic, parsley, salt, pepper, and spinach, stirring until mixed.

Place a warm tortilla on a flat surface, spoon 1/2 cup of filling in the center, and roll tightly.

Cook wraps seam-side down in the skillet for 2-3 minutes. Flip to achieve golden brown on both sides.

Remove from skillet, cool for a minute, slice diagonally, and serve garnished with parsley.