Preheat the oven to 350 degrees F.
Put the peanuts in a shallow pan and bake for 10 minutes. Let cool and chop coarse. Coarsely grate the carrots. Heat the oil in a large wok or skillet over high heat until hot but not smoking. Add the carrots and cook, stirring constantly, until cooked evenly, about 5 minutes. Stir in the peanuts and pepper flakes and season with salt and pepper. Finish with a squeeze of lime juice and serve hot.