1. Cook noodles according to package directions; drain, and set aside.
2. Combine warm water and tamarind paste in a 2-cup measuring cup, stirring until dissolved. Stir in brown sugar, fish sauce, and chili-garlic sauce. Set aside.
3. Heat wok over high heat until a few drops of water evaporate immediately. Swirl 2 tablespoons oil in pan to coat. (If using a nonstick skillet, heat oil over medium-high heat.) Add garlic; cook 30 seconds. Add shrimp, and cook, stirring often, 3 minutes or until done. Transfer shrimp to a plate.
4. Heat 1 tablespoon oil in wok over high heat (medium-high, if using a nonstick skillet). Add reserved noodles and half of sauce mixture. Cook 1 minute, separating noodles with tongs.
5. Push noodles to edges of wok, forming a well in the center. Pour remaining 1 teaspoon oil into well; pour egg into oil, and cook, stirring, until done. Stir in carrots, green onions, remaining sauce mixture, and 1/2 cup bean sprouts. Cook 1 to 2 minutes or until heated through. Top with peanuts, cilantro, and remaining 1/2 cup bean sprouts; serve immediately with lime wedges.
*Tamarind paste adds bright, sour flavor to this iconic noodle dish. Substitute fresh lemon or lime juice, if necessary.