Coat the flank steak with 3 tablespoons of the soy sauce in a shallow dish and marinate for 30 minutes, turning once. Cut the meat across the grain into very thin slices.
Prepare an ice bath by filling a large bowl with water and ice. Bring a large pot of lightly salted water to a boil. Add the snap peas and cook until crisp-tender, about 1 minute. Remove the peas from the water with a slotted spoon, reserving the boiling water, and transfer to the ice bath to cool. Drain and set aside.
Cook the noodles in the boiling water for 1 minute less than directed on the package, or until they are al dente; they will be cooked more when fried. Drain well and transfer to a bowl. Toss the noodles in the sesame oil and the remaining 3 tablespoons soy sauce. Set aside until ready to fry.
Heat 3 tablespoons of the peanut oil in a large nonstick skillet over medium heat. Add the noodles and flatten them into a pancake using the back of a spatula. Cook without stirring for 5 minutes, until lightly browned. Flip over and cook the other side in the same way. Transfer to a plate and keep warm.
Heat 1 tablespoon of the peanut oil in the skillet over high heat; add the snap peas and stir-fry for 2 minutes. Add the water; cover and steam for 1 minute. Transfer to a plate with a slotted spoon.
Wipe out the skillet with a paper towel. Heat the remaining tablespoon of peanut oil in the skillet over medium heat. Add the yellow onion and stir-fry for 4 minutes, until soft and golden. Add the meat to the skillet and stir-fry for 5 minutes. Add the oyster sauce and the cornstarch mixture. Stir to combine and cook for 1 to 2 minutes longer, until the sauce is thickened to the consistency of gravy.
Divide the noodles into 6 portions and top each with some of the sugar snap peas and beef; garnish with the green onions.