1/4 cup lower-sodium soy sauce
3 tablespoons oyster sauce
2 tablespoons mirin
2 1/2 teaspoons light brown sugar
1 teaspoon toasted sesame oil
1 pound small peeled, deveined raw shrimp
3 tablespoons neutral cooking oil, divided
5 scallions, trimmed and cut crosswise into 2-inch pieces (about 1 cup), plus thinly sliced scallions for garnish
2 cups sliced stemmed fresh shiitake mushrooms (about 5 ounces)
1 1/2 cups chopped green cabbage
1/2 cup thinly sliced carrot
1 tablespoon finely chopped garlic
3 (9-ounce) portions frozen udon, thawed

Whisk together soy sauce, oyster sauce, mirin, brown sugar, and sesame oil in a small bowl until well combined and sugar dissolves. Set aside.

Pat shrimp dry using paper towels. Heat 1 tablespoon neutral oil in a wok or large cast-iron skillet over medium-high until shimmering. Add shrimp; cook, stirring often, until pink and just cooked through, 2 to 3 minutes. Transfer shrimp to a bowl.

Add remaining 2 tablespoons neutral oil to skillet. Add scallions and mushrooms to skillet; cook over medium-high, stirring often, until just starting to brown, 2 to 3 minutes, adjusting heat as needed to prevent overbrowning. Add cabbage, carrot, and garlic; cook, stirring constantly, until vegetables are starting to soften, 3 to 4 minutes.

Add udon, soy sauce mixture, and shrimp to skillet, stirring to coat. Cook, stirring constantly, over medium-high until noodles are tender and sauce is absorbed, about 2 minutes.