1. Cut the chicken and onions into strips. Sprinkle with spices and salt. In a pan, heat the oil and brown on all sides. Remove the skin from the avocados and cut the flesh into strips. Drizzle with lime juice. Season with salt and pepper.
2. Grate the carrots and cut the tomatoes into thin wedges.
3. Option 1: Warm the tortillas in the microwave or in a pan. Optionally spread them with a sauce of your choice, sour cream, or cream cheese. Fill them with a lettuce leaf, avocado, sliced chicken, grated cheese, tomatoes, carrots, and torn basil leaves. Roll them up and serve immediately.
4. Option 2: Optionally spread them with a sauce of your choice, sour cream, or cream cheese. Fill them with avocado, sliced chicken, tomatoes, carrots, and torn basil leaves. Roll them up and serve immediately.
Place the rolled fajitas in a baking dish. Sprinkle with some grated cheese and broil for a few minutes until melted. Serve with a side of green salad.