Start by preheating a skillet or grill pan over medium heat. Add a drizzle of olive oil, ensuring the surface is evenly coated.

In a mixing bowl, combine shredded cooked chicken breast, mozzarella cheese, cheddar cheese, cream cheese, minced garlic, fresh parsley, salt, and pepper. Stir until all ingredients are thoroughly mixed.

Lay out your low-carb tortillas on a clean surface. Divide the cheesy chicken mixture evenly among the tortillas, placing it towards one end. Carefully roll each tortilla tightly.

Place the assembled wraps seam-side down in the preheated skillet. Cook for 2-3 minutes, then flip and cook for an additional 2-3 minutes until crispy and the cheese has melted.

Once cooked, remove the wraps from the skillet and let them cool slightly. Slice each wrap in half and serve hot, garnishing with additional fresh parsley.