In a mixing bowl, combine shredded chicken, mozzarella cheese, cream cheese, minced garlic, and chopped parsley. Stir until the mixture is creamy and evenly blended, about 2-3 minutes.

Season the filling with salt and pepper to taste. Mix thoroughly after adding the seasoning, ensuring the flavors are well-distributed. This step should take another minute or so.

Lay out the tortillas and evenly distribute the chicken mixture onto each tortilla, leaving about an inch of space at the edges. This step should take about 5 minutes.

Carefully roll each tortilla, starting from one edge and tucking the filling as you go. Fold in the sides to secure the filling and roll tightly to prevent leakage. This should take about 3-5 minutes.

In a skillet, heat 2 tablespoons of olive oil over medium heat until it shimmers, approximately 2 minutes.

Carefully place the wraps seam-side down into the hot skillet and cook for 3-4 minutes on one side. Flip them over and continue to cook for an additional 3-4 minutes until golden and crispy.

Once cooked, remove the wraps from the skillet and let them cool slightly on a paper towel-lined plate. Cut each wrap in half for easy serving.