Preheat a large skillet over medium heat for about 2 minutes, adding olive oil until shimmering.

Microwave low-carb tortillas wrapped in a damp paper towel for 10-15 seconds until softened.

In a large mixing bowl, combine the shredded chicken, mozzarella, cheddar, cream cheese, minced garlic, and fresh parsley. Add salt and pepper to taste, mixing until well combined.

Take a warm tortilla and place about 1/2 cup of the filling in the center, rolling tightly and tucking in the sides.

Cook the wraps seam-side down in the skillet for 2-3 minutes until golden brown, flipping halfway for even cooking.

Remove from the skillet and let cool slightly before slicing each wrap diagonally and serve hot.