Cut steak into thirds with grain, then slice each third thin against grain.
Whisk 1 tablespoon oyster sauce, 1 tablespoon cornstarch, water, and baking soda together in medium bowl.
Add beef, stir to coat, and let sit at room temperature for 15 to 30 minutes.
Combine scallion whites, 2 tablespoons oil, garlic, and ginger in second bowl.
Whisk broth, soy sauce, sugar, remaining 3 tablespoons oyster sauce, and remaining 1 ½ teaspoons cornstarch together in third bowl.
Heat remaining 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until just smoking.
Add beef to skillet and break up clumps with tongs. Cook, without stirring, until beef is browned on bottom, about 2 minutes. Stir and continue to cook until beef is spotty brown and no longer pink, about 2 minutes longer, stirring occasionally.
Stir in scallion mixture and cook until fragrant, about 1 minute.
Whisk broth mixture to recombine.
Add broth mixture and broccoli to skillet, cover, and cook until broccoli is crisp-tender, about 3 minutes, shaking skillet occasionally to redistribute contents.
Off heat, stir in scallion greens. Serve.
