Heat oil in a pan, and splutter mustard seeds and curry leaves. Sauté shallots, garlic, and green chilly until the shallots become soft. Add ground turmeric and fry for 2 seconds. Now throw in grated carrot and mix well. Cover with lid, and allow it to cook. Remember to stir occasionally.
When the carrot is almost done, add eggs. Stir continuously until the eggs are cooked. Season with salt and pepper.