1Pat the shrimp dry. Separate the bok choy stems from the leaves, slice the stems, and roughly chop the leaves. Slice the shiitake mushrooms if they are not already sliced.
In a small bowl, combine the low-sodium soy sauce and mirin. Set the sauce aside.
Heat 1 tablespoon of vegetable oil in a large wok or deep skillet over medium-high heat. Add the shrimp in a single layer and cook for 1–2 minutes per side, until pink and just cooked through. Transfer the shrimp to a plate.
Add the remaining 1 tablespoon of vegetable oil to the same pan. Add the shiitake mushrooms and bok choy stems, then stir-fry for 3–4 minutes until lightly browned and beginning to soften.
Add the bok choy leaves and cook for 1–2 minutes, stirring frequently, until wilted but still bright green.
Reduce the heat to medium. Add the unsalted butter and minced garlic, then cook for about 30 seconds while stirring, just until fragrant. Do not let the garlic burn.
Add the cooked udon noodles and the prepared soy-mirin sauce. Toss for 2–3 minutes, separating the noodles as needed, until they are hot and evenly coated.
Return the cooked shrimp to the pan and add most of the sliced scallions. Toss for 1 minute, until the shrimp is heated through and everything is coated in the garlic butter soy sauce.
Remove from the heat, garnish with the remaining sliced scallions, and serve immediately.