Put the noodles in a bowl and add enough hot water to cover. Soak them until tender, approx. 30 minutes. Drain and set them aside. Whisk the sugar with the fish sauce and vinegar in a small bowl.
Heat a large skillet over medium heat until hot and then add 1 T. of the peanut oil. Pour in the eggs, tilting the skillet as you pour to make a thin, even coating of egg. Cook until just set, approx 45 seconds. Invert the eggs onto a cutting board and cut into 1/2-inch pieces. Set aside.
Add another 1 T. of the peanut oil to the same skillet and heat over high heat. Add shrimp, 1/2 t. of the pepper flakes, and salt to taste. Stir-fry until the shrimp are pink and just cooked through, about 1 1/2 minutes. Transfer to a plate.
Heat the remaining 2 T. of peanut oil over high heat. Add the garlic, shallots, and remaining 1/4 t. red pepper flakes and stir-fry until lightly browned, approx. 1 minute. Add the tofu and cook for about 2 minutes more. Add the noodles and cook, tossing, until lightly coated with the garlic mixture, approx. 1 minute. Add the fish sauce mixture and the large scallion pieces and heat through. Stir in the cooked egg and shrimp, 1 C. of the sprouts, and the 1/3 C. peanuts and toss until it is all hot.
Divide the phad Thai among the plates and top with the remaining 1/4 C. sprouts, additional peanuts, and chopped scallions. Serve right away with the lime wedges and Sriracha.