Cut steak lengthwise with grain into thirds, then slice each third against grain ¼ inch thick.
Whisk 1 tablespoon oyster sauce, cornstarch, 1 tablespoon soy sauce, and baking soda together in large bowl.
Add steak and toss to thoroughly coat.
Whisk water, sugar, remaining 3 tablespoons oyster sauce, and remaining 1 tablespoon soy sauce together in small bowl; set aside.
Heat 1 tablespoon oil in 12-inch nonstick skillet over high heat until just smoking.
Add beef to skillet, breaking up clumps with tongs, and cook, without stirring, until beginning to brown, about 4 minutes.
Stir and continue to cook until beef is spotty brown and no longer pink, about 4 minutes longer.
Stir in scallion whites, garlic, and oyster sauce mixture.
Top with bok choy; cover and cook until bok choy is tender, about 4 minutes, shaking skillet occasionally.
Sprinkle with scallion greens and drizzle with remaining 1 tablespoon oil. Serve.
