In a small bowl, mix soy sauce, sake, mirin, oyster sauce, and dark brown sugar until the sugar dissolves. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken breast and cook it‘s no longer pink (7 minutes). Season with salt and freshly ground black pepper. Remove from the pan and set aside.
In the same pan, add a little more oil if needed. Add the ginger slices and stir-fry until tender. Add the chopped spring onion, julienned carrot, thinly sliced leek, roughly chopped bok choy, and bean sprouts. Stir-fry for 2-3 minutes until the vegetables are tender but still crisp.
When the water is boiling, blanch 2 servings udon noodles for 30–40 seconds or until it just starts to loosen up. If you‘re using dry udon noodles, boil them according to the package instructions. Transfer the noodles to a plate and set aside.
Return the cooked chicken to the pan. Add the cooked udon noodles and pour the prepared sauce over everything. Toss well to evenly coat the noodles, chicken, and vegetables with the sauce. Cook for 1-2 minutes to heat through.
Transfer to plates or bowls and serve immediately. Garnish with additional spring onion, sesame seeds, or a drizzle of sesame oil if desired.