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Step 1
In a small bowl, whisk together the soy sauce, broth or water, 1 tablespoon cornstarch and the brown sugar until combined.
Step 2
Cut the flank steak with the grain into 2-inch-wide pieces, then slice against the grain into 1/8-inch-thick strips. Place the steak on a large plate and sprinkle with the remaining 1 tablespoon cornstarch. Toss to coat.
Step 3
In a large flat-bottomed wok, or nonstick or well-seasoned cast-iron skillet over medium-high heat, heat 2 tablespoons of the oil until shimmering but not smoking. Add the steak and cook, stirring frequently, until browned, about 4 minutes. Transfer the steak to a plate.
Step 4
Add the remaining 1 tablespoon of oil to the pan and heat until just smoking. Add the onion, broccoli and carrot to the pan. Cook, stirring, until the onion softens and broccoli and carrot are slightly tender, about 3 minutes.
Step 5
Stir in the scallions, garlic and ginger. Cook, stirring, just until fragrant, about 30 seconds. Whisk the soy sauce mixture again. Reduce the heat to medium and add the soy mixture and beef to the pan. Cook until the sauce thickens, about 1 minute.
Step 6
Serve over cooked brown rice or with steamed riced cauliflower and garnish with toasted sesame seeds and additional scallions, if desired.