In a small bowl combine soy sauce, brown sugar, garlic, ginger and black pepper; set aside.
Cook the noodles according to the package directions. Drain. Rinse noodles, drain, and place noodles in a large bowl. Add soy sauce mixture, and toss to coat. Set aside.
Heat oil in a large skillet or wok over medium-high heat. Once the oil is hot, add onion and sauté until soft and transparent, about 5-7 minutes. Add cabbage and sauté until cabbage is soft, with browned edges, about 10 minutes. Add carrots and sauté for 2-3 minutes until all veggies are softened.
Toss cooked veggies into the large bowl with the cooked noodles and mix well.
Udon noodles can be served hot at this point, or cooled and refrigerated until ready to serve cold. Also, noodles can be cut into smaller pieces so they are easier to serve and eat, if desired.