Place flank steak in freezer for 10-15 minutes, then slice against the grain into 1/4 inch (6mm) strips.
Combine sliced beef with 1 tablespoon soy sauce, baking soda, and 1 tablespoon cornstarch. Massage until liquid is absorbed and let sit at room temperature for 15 minutes.
Cut broccoli into bite-sized florets. Mince garlic and ginger, and slice scallions for garnish.
Whisk together remaining soy sauce, oyster sauce, beef broth, and brown sugar until sugar dissolves. In a small dish, mix remaining cornstarch with 2 tablespoons cold water to make a slurry. Stir in sesame oil last.
Heat 2 tablespoons vegetable oil in wok over high heat until shimmering. Add beef in a single layer (working in batches if needed) and sear for about 1 minute per side until browned but still slightly pink in center. Remove to a plate.
Add remaining tablespoon oil to the same wok over medium-high heat. Add broccoli florets with 2 tablespoons water, cover, and steam for 2-3 minutes until bright green and just tender. Push broccoli aside and add garlic and ginger, stirring for 20 seconds until fragrant.
Return seared beef and any juices to the wok. Whisk sauce mixture again, pour over beef and broccoli, and bring to a simmer. Stir cornstarch slurry once more before adding to the pan. Stir constantly for 1-2 minutes until sauce thickens to a glossy coating consistency.
Remove from heat immediately. Taste and adjust with extra soy sauce if needed. Serve over rice and garnish with sesame seeds and sliced scallions if using.