Place a large pan over medium heat (no higher than medium if you are using coconut oil). Add coconut oil.
Add carrots to pan and saute 2-3 minutes. Add cabbage, peppers and kale, and saute for 3-4 more minutes until veggies are bright with color and a little softened.
Crack egg directly into pan, let it cook for 1 minutes, then use a spatula to break the egg up and toss with vegetables.
Remove pan from heat, and sprinkle salt and nutmeg over vegetable and egg mixture.
Serve in a large bowl topped with walnuts.