In a large mixing bowl, combine the shredded chicken, mozzarella cheese, cream cheese, minced garlic, and chopped parsley. Mix thoroughly until creamy.

Season the mixture with salt and pepper to taste, mixing well for even distribution.

Lay out tortillas and distribute chicken filling evenly across each, leaving an inch at the edges.

Roll the tortillas tightly, tucking in the sides as you go to maintain the filling.

In a large skillet, heat olive oil over medium heat until shimmering.

Place wraps seam-side down, cooking for 3-4 minutes until golden brown, then flip to brown the other side.

Remove wraps and let cool slightly. Slice in half to reveal filling and serve warm with dipping sauces.