Saute peppers and onions in a small amount of oil. Add cilantro and parsley, season with salt and pepper. Cook until tender. Reserve. Combine eggs and milk. Mix well and reserve.
Heat a non-stick omelette or egg pan over medium heat. Portion beaten egg into pan. Stir in sauteed pepper and onion. Cook until set. Flip omelette and cook until done. Add sliced avocado and top with cheese. Fold omelette and turn out onto warm serving plates.
Top with additional cheese and garnish with fresh cilantro sprigs.
