Submerge rice noodles in a large bowl filled with hot water. Let rest until soft and white, about 20 minutes.
In a medium bowl, combine lime juice, tamari, brown sugar, water, and garlic; whisk until sugar dissolves.
Cut string beans and scallions into 1-inch pieces. Place a wok or large skillet over medium-high heat. When hot, add oil, swirling to coat inside of pan. Add string beans and scallions; stir-fry 5 minutes. Add tofu and egg; stir-fry 3 minutes.
Drain noodles and add to pan, along with bean sprouts and lime juice mixture. Cook, tossing with tongs, until noodles are soft and mixture is heated through, about 5 minutes. Spoon into shallow bowls. Sprinkle with cilantro and peanuts and garnish with lime wedges.