Heat oil in a wok over medium-high heat. Add carrots and cook until they begin to soften. Add salt and sugar. Cook until tender but still has bite. Set aside.
In the same wok, cook the beef, breaking it into small pieces. Blot any excess liquid with a paper towel. When mostly browned with a little pink remaining, add soy sauce and sugar. Cook until just done but still moist. Set aside.
Without washing the wok, fill it with water and bring to a boil. Cook somyeon according to the package directions (about 3 minutes). Drain, then rinse under cold running water, rubbing the noodles until cooled. Drain well.
Rinse wok. Add noodles, carrots, beef, and remaining ingredients. Toss until evenly coated. Top with seasoned seaweed and an extra drizzle of sesame oil.
