Put the noodles in a large bowl and cover with cold water. Set aside until pliable and al dente, 45 to 60 minutes. Drain well.
Meanwhile, make the sauce: Break the tamarind paste into bits with your fingers and put in a small bowl. Cover with 1/4 cup boiling water and let stand 10 minutes. Mash with a fork to break up the paste, then press through a fine-mesh sieve with a rubber spatula over a bowl, discarding any seeds and tough bits. Stir in the sugar, fish sauce and a pinch of salt until smooth; set aside.
Heat a large cast-iron skillet over medium heat. Add 2 tablespoons vegetable oil, then add the tofu, shallot, ginger and garlic. Cook, stirring with a flat wooden spoon, until tender but not browned, about 2 minutes. Add the noodles and a few tablespoons of the tamarind sauce. Cook, stirring and spreading the noodles around the skillet, until the noodles absorb all the sauce, about 1 minute. Add a few more tablespoons of the tamarind sauce and stir-fry 30 seconds to 1 minute more.
Push the noodle mixture to one side of the skillet and add the remaining 1 tablespoon vegetable oil to the other side. Add the shrimp to the oil in a single layer and cook until mostly pink but not quite cooked through, 2 to 3 minutes. (Occasionally stir the noodles to make sure they are not sticking to the skillet.) Add the remaining tamarind sauce and stir to combine the noodles and shrimp.
Push the noodle-shrimp mixture to one side of the skillet. Add the eggs to the other side, stir briefly, then let cook, undisturbed, until mostly set. Spoon the noodle-shrimp mixture on top of the eggs, then flip the whole thing over and break up the eggs into large chunks. Remove from the heat, add the bean sprouts and scallions and stir quickly to combine (you want the sprouts and scallions to remain crunchy). Divide among bowls, top with the peanuts and serve with lime wedges.