Whisk together oyster sauce, soy sauce, mirin, rice vinegar, Worcestershire, sesame oil, sugar, Sriracha, and garlic in a small bowl; set aside. Remove root ends from scallions and discard. Chop whites and light greens into 2-inch pieces and quarter pieces lengthwise; set aside. Thinly slice remaining dark greens of scallions and reserve for garnish.
Heat oil in a large skillet or wok over medium-high heat. Add mushrooms in a single layer and cook, undisturbed, until browned on first side, about 3 minutes. Stir and continue to cook, stirring occasionally, until mushrooms are tender and golden brown on both sides, about 4 more minutes. Add bok choy, carrots, sliced whites and light greens of scallions, and 1/4 cup water to pan with mushrooms. Cook, stirring occasionally, until vegetables are just tender, about 3 minutes.
Add udon noodles and remaining 1/4 cup water and cook, gently separating noodles with tongs or spoon. Add reserved oyster sauce mixture and cook, stirring constantly, until noodles and vegetables are well-coated, about 1 minute. Divide among serving bowls and garnish with reserved sliced greens of scallions and optional garnishes. Serve immediately. Recipe developed by Marianne Williams
