Soak the rice noodles in warm water for 30 minutes, then drain and set aside.
Heat 1 tablespoon of oil in a wok or large skillet over medium heat. Add the shrimp and cook until pink, about 2-3 minutes. Remove from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Pour in the beaten egg and scramble until cooked through. Push the egg to one side of the skillet.
Add the soaked noodles, bean sprouts, and chopped vegetables to the skillet. Stir-fry for 2-3 minutes until the vegetables are tender.
In a small bowl, combine the fish sauce, tamarind paste, and brown sugar. Pour this sauce over the noodles and vegetables, stirring well to coat.
Return the cooked shrimp to the skillet and toss everything together until well combined and heated through.
Serve the Pad Thai hot, garnished with chopped peanuts and lime wedges on the side.