In a large bowl, combine shredded chicken, mozzarella cheese, cream cheese, minced garlic, and chopped parsley. Mix until creamy and well-blended.

Sprinkle salt and pepper over the mixture and stir well. Taste and adjust seasoning as needed.

Lay out tortillas on a clean surface. Divide the chicken mixture evenly across each tortilla, leaving space on the edges.

Carefully roll each tortilla tightly around the filling, tucking in the edges as you go and securing the filling.

In a skillet, heat a tablespoon of olive oil over medium heat until shimmering, about 2 minutes.

Place the wraps seam-side down in the skillet and cook for 3–4 minutes until golden brown. Flip and cook for another 3–4 minutes.

Remove wraps from the skillet, slice in half, and serve warm with dipping sauces.