In a large mixing bowl, combine shredded chicken, mozzarella cheese, cream cheese, minced garlic, and chopped parsley. Stir until all ingredients are evenly mixed, achieving a creamy consistency.

Sprinkle salt and pepper into the filling mixture to taste, integrating these essential seasonings thoroughly.

Lay out your tortillas on a clean, flat surface. Evenly distribute the chicken filling mixture onto each tortilla, keeping an inch of space around the edges.

Gently fold in the sides of each tortilla and roll them tightly from the bottom to the top to secure the filling inside.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Ensure the oil shimmers, signifying it is hot enough for frying.

Place the prepared wraps seam-side down in the hot skillet, cooking for about 3-4 minutes or until they turn golden brown and crispy.

Once crispy and golden, carefully remove the wraps from the skillet and let them cool for a minute. Slice each wrap in half and serve warm.