Bring a large pot of salted water to a boil. Meanwhile, whisk together ingredients for sauce.
When water is boiling, add noodles and cook for 4-5 minutes, until noodles are just al dente (set a timer, you don't want soggy noodles - they'll continue cooking a bit later). Drain in a colander and run cold water over top to stop cooking. Reserve the pot.
Heat 2 tbsp oil in a large skillet over medium-high heat. Whisk eggs with a good pinch of salt. When oil is shimmering hot, add eggs, tilting pan to evenly coat bottom. When eggs are set, fold over onto itself and transfer to a plate. Slice thinly crosswise.
Add another tablespoon oil to skillet. Season tofu cubes with a good sprinkle of salt, tossing to season on all sides. Add to skillet and cook, turning until golden brown on all sides. Transfer to plate with eggs.
Add shrimp to pan and cook until opaque. Transfer to plate with eggs and tofu.
Add 2 tbsp oil to the empty noodle pot over medium-high heat. Add onion and cook until golden, about 2 minutes. Add snow peas, season with salt, and cook until bright green, about 2 minutes more. Add carrot, noodles, sauce, tofu, egg and shrimp to pot. Cook, tossing with tongs, until everything is evenly coated with sauce and noodles are heated through.
Serve topped with sprouts, cucumber, peanuts, green onions, cilantro and lime wedges for squeezing.