Bring 3 quarts water to a boil in a large Dutch oven. Cut bok choy diagonally into 1-inch pieces; separate green portions and stalks. Cook stalks in boiling water 2 minutes. Add green portions; cook 1 minute. Remove bok choy from water with a slotted spoon; place in a colander. Rinse under cold water; drain. Place in a bowl.
Return water to a boil, and add soba. Cook 4 minutes or until al dente. Drain and rinse with warm water; drain.
Heat olive oil in a wok or large nonstick skillet over medium-high heat. Add garlic chives to pan; stir-fry 10 seconds. Add shiitake and cremini mushrooms and sake; cover, reduce heat to medium-low, and cook 3 minutes or until mushrooms are tender. Uncover and increase heat to medium-high. Add bok choy and soy sauce; cook 2 minutes, stirring occasionally. Add noodles; cook 2 minutes, tossing to combine. Serve immediately.