Preheat a skillet over medium heat, adding 1 tablespoon of olive oil and heating until shimmering.

Warm low-carb tortillas on a microwave-safe plate, covered with a damp paper towel for 10-15 seconds.

In a bowl, mix the shredded chicken, mozzarella, cheddar, cream cheese, garlic, parsley, and season with salt and pepper.

Scoop about ½ cup of the chicken mixture into a warmed tortilla and roll tightly.

Place wraps seam-side down in the skillet; cook for 2-3 minutes on each side until golden brown.

Remove from skillet, let rest for a minute, slice diagonally, and serve hot.