In a large mixing bowl, combine shredded chicken, mozzarella cheese, cream cheese, minced garlic, and chopped parsley. Blend everything until well incorporated.

Carefully sprinkle salt and pepper over the filling mixture, adjusting seasoning to taste. Mix again until seasoning is thoroughly blended.

Lay out tortillas on a clean surface. Spoon a generous amount of the chicken mixture onto each tortilla, leaving a small border at the edges.

Starting from one end, roll the tortilla tightly, tucking in the sides as you go. Repeat this with all tortillas, arranging wraps seam-side down.

In a skillet, heat olive oil over medium heat until shimmering. Place the wraps seam-side down into the pan and cook for about 3-4 minutes until golden brown. Flip to cook the opposite side.

Once wraps are perfectly crisp, remove from skillet and let rest. Slice each wrap in half diagonally to show the filling. Serve warm.