In a small bowl, stir together the oyster sauce, dark soy sauce, mirin, brown sugar, and gochugaru or red pepper flakes, if included. Continue mixing until the sugar is incorporated. Lightly season the shrimp with salt and black pepper, then set it aside.
Place the frozen udon portions in a heat-resistant bowl and cover them with hot water. Allow the noodles to stand for approximately 1 minute, then carefully separate the strands with chopsticks. Rinse them under cold running water, drain thoroughly, and reserve.
Warm 1 tablespoon of the cooking oil in a wok or large frying pan over medium heat. Add the seasoned shrimp and stir-fry for about 2 minutes, or until fully cooked and opaque. Transfer the shrimp to a plate and set aside.
Pour the remaining tablespoon of oil into the same wok. Add the sliced onion and minced garlic, then cook for approximately 1 minute, stirring frequently, until aromatic.
Add the cabbage, carrot, and mushrooms. Continue stir-frying for 2 to 3 minutes, or until the vegetables begin to soften while retaining some texture.
Return the cooked shrimp to the wok. Add the drained udon noodles and pour in the prepared sauce.
Toss the ingredients continuously over medium heat until the noodles are evenly covered with sauce and heated throughout. Add the chopped scallions and stir briefly to distribute them.
Divide the stir-fried udon between serving plates. Garnish as desired with Kewpie mayonnaise, bonito flakes, toasted sesame seeds, and additional sliced green onions. Serve immediately.