Make the sauce: Pour 1/4 cup boiling water over the brown sugar in a bowl and stir to dissolve. Add the lime juice, fish sauce, rice vinegar and Sriracha and stir to combine. Add the cooked turkey to the sauce and let it absorb the flavors while prepping the rest of the dish.
Bring a pot of salted water to a boil. Add the linguine and cook 1 minute less than the label directs. Drain and set aside.
Heat the vegetable oil in a wok or large sauté pan over high heat until very hot, almost smoking. Add the onion and stir-fry 1 minute. Add the garlic and stir, then add the eggs and cook for 30 seconds, stirring. Add the linguine and turkey (with the sauce) and cook, stirring, for a few minutes. Remove from the heat and toss in the grated carrot, peanuts, cilantro, bean sprouts and scallions. Serve with lime wedges.