Cover the noodles with hot tap water (not boiling) in a large bowl and soak until softened, pliable, and limp but not fully tender, about 20 minutes. Drain the noodles and set aside.
While the noodles soak, stir the lime juice, water, fish sauce, rice vinegar, brown sugar, and 2 tablespoons of oil together and set aside. Prep and measure out the rest of the ingredients while the noodles are soaking.
Pat the shrimp dry with paper towels. Heat 1 more tablespoon of oil in a 12-inch nonstick skillet over high heat until just smoking. Add the shrimp, spread into single layer, and cook without stirring for 1 minute. Stir the shrimp and continue to cook until spotty brown and just pink around the edges, about 30 seconds. Transfer the shrimp to its own bowl, cover, and set aside.
Add the remaining tablespoon of oil and garlic to the skillet and return it to medium heat until fragrant, about 30 seconds. Add the eggs and 1/4 teaspoon salt and cook, stirring vigorously until the eggs are scrambled, about 20 seconds.
Stir the soaked noodles into the eggs. Add the fish sauce mixture, increase heat to high, and cook, tossing constantly, until the noodles are evenly coated. Add ¼ cup of peanuts, bean sprouts, all but 1/4 cup of scallions and cooked shrimp. Continue to cook, tossing constantly, until the noodles are tender, about 2 minutes (if not yet tender, add 2 tablespoons of water to the skillet and continue to cook until tender).
Transfer the noodles to a serving platter and sprinkle with the remaining scallions and peanuts. Serve, passing lime wedges and chopped cilantro.
Notes
Be sure to use the wide, fettuccine-style rice noodles.
For spicy noodles, add a pinch of cayenne to the finished dish or serve with tabasco.