In a small bowl, mix together dark soy sauce, oyster sauce, mirin, brown sugar, and rice wine vinegar until the sugar dissolves. Set it aside.
Place a large wok or skillet on the stove over medium-high heat. Once it's hot, add cooking oil, onions, and garlic. Fry for 2-3 minutes, stirring occasionally, until the onions are translucent.
Add ground chicken, salt, pepper, and 1-2 tablespoons soy sauce mixture to the wok. Using a spatula or wooden spoon, break the ground chicken into smaller pieces. Spread the chicken evenly around the wok. Cook for 6-7 minutes, stirring occasionally, until browned and fully cooked. Transfer the cooked chicken to a separate plate and set it aside.
Add more oil to the wok and sauté the mushrooms for 2 minutes on each side. Add the bok choy and carrots (or vegetable of choice) and let it cook for 2-3 minutes until they are heated through but still slightly crunchy.
Toss in the udon noodles and the rest of the sauce. Add a splash of water, if needed, to rehydrate the noodles. Stir fry until veggies and noodles are cooked to your desired texture, around 3-4 minutes.
