Soak the dried rice noodles in cool or lukewarm water for 30 minutes, or until they're limp but still firm to the touch; later cooking in the wok will soften them more. Drain the noodles thoroughly in a colander and set aside while preparing the other ingredients.
In a small bowl, mix the fish sauce, tamarind juice, and sugar; stir well to melt the sugar. Taste and adjust flavors to the desired combination of salty, sour, and sweet.
Heat a wok over medium-high heat until it is smoking hot. Add 1 tablespoon of the oil and quickly stir-fry the shrimp until they turn pink and are almost cooked through; 1 to 2 minutes. Remove the shrimp to a plate and cover to keep warm.
Add the remaining oil to the wok and toss in the garlic, shallots, and chile; stir-fry for 30 seconds. Push the garlic and shallots to 1 side of the wok and pour the egg into the center. Scramble the egg lightly until set, breaking it up into pieces with a spatula. Add the drained noodles to the wok, stirring and tossing quickly with 2 spatulas to separate the strands. Pour in the fish sauce mixture, tossing well to coat the noodles and keep them from sticking (if the noodles are still too firm, drizzle with 1 to 2 tablespoons of water to help them cook.)
When the noodles are in good shape, toss in 1/2 of the bean sprouts and peanuts; save the remaining for garnish. Continue to stir-fry, to combine. Return the shrimp to the wok and toss the pad thai together to warm everything through. Serve the pad thai on a platter, pile the remaining bean sprouts and peanuts on 1 side of the dish and garnish with the lime wedges and cilantro. Squeeze lime juice over each portion before eating.