Combine white parts of the green onions, red chile pepper, green chile pepper, and garlic in a large bowl. Add dark soy sauce, 3 tablespoons walnut oil, and brown sugar; mix marinade well. Add beef to marinade, cover, and refrigerate for a minimum of 15 minutes and up to 24 hours.
Bring a large pot of salted water to a boil. Add egg noodles; cook until softened but still firm to the touch, 2 to 3 minutes. Drain.
Cook spinach in a separate pot of boiling, lightly salted water until wilted, 3 to 5 minutes. Drain and set aside.
Heat 1 teaspoon walnut oil in a wok. Add green parts of the green onions, bell pepper, snow peas, baby corn, and 1/2 teaspoon soy sauce. Stir-fry until lightly browned, yet still crisp, 2 to 3 minutes. Remove from the wok.
Stir-fry noodles, 1 teaspoon oil, and 1/2 teaspoon soy sauce in the same wok until crisp, 1 to 2 minutes. Transfer to a plate.
Heat 1 teaspoon oil in the wok and stir-fry marinated beef and some of the sesame seeds in batches until fully cooked, 3 to 4 minutes. Add cooked vegetables back to the wok and stir-fry until heated through, about 2 minutes.
Place a light layer of drained spinach over the noodles and pour stir-fry mixture on top.