Preheat a nonstick skillet or grill pan over medium heat for about 3-5 minutes. Drizzle in the olive oil and let it warm up until it shimmers slightly. Warm the low-carb tortillas in the microwave for 10-15 seconds.

In a mixing bowl, combine cooked and shredded chicken breast, shredded mozzarella, shredded cheddar, softened cream cheese, minced garlic, and a sprinkle of salt and pepper. Stir the mixture thoroughly until well-blended.

Take each warm tortilla and place about ½ cup of the cheesy chicken filling in the center. Roll the tortilla tightly, tucking the filling in as you go.

Place the wraps seam-side down in the preheated skillet. Cook for about 2-3 minutes on each side, flipping once, until golden-brown and the cheese starts to ooze.

Remove the wraps from the skillet, slice in half diagonally, and arrange on a serving plate. Garnish with chopped fresh parsley if desired. Serve hot.