For the sauce:

Whisk all ingredients together in bowl.

For the stir fry:

Combine beef and soy sauce in bowl, cover, refrigerate, and let marinate for at least 10 minutes or up to 1 hour. Drain beef and discard liquid. In separate bowl combine garlic, ginger, and 1 teaspoon oil.

Heat 12-inch cast-iron skillet over medium heat for 5 minutes. Add 1 tablespoon oil and heat until just smoking. Add half of beef, break up any clumps, and cook, without stirring, for 1 minute. Stir beef and continue to cook until browned, about 2 minutes; transfer to bowl. Repeat with 1 tablespoon oil and remaining beef; transfer to bowl.

Heat 1 tablespoon oil in now-empty skillet over medium-high heat until just smoking. Add broccoli and cook for 30 seconds. Add 1/3 cup water, cover, and reduce heat to medium. Steam broccoli until crisp-tender, about 2 minutes; transfer to paper towel–lined plate.

Wipe skillet clean with paper towels. Heat remaining 2 teaspoons oil in now-empty skillet over medium-high heat until just smoking. Add bell pepper and onion and cook, stirring often, until bell pepper’s are spotty brown, about 1-1/2 minutes.

Clear center of skillet, add garlic mixture, and cook, mashing mixture into skillet, until fragrant, about 30 seconds.

Add broccoli, onions, beef, and any accumulated beef juices and toss to combine. Whisk sauce to recombine, then add to skillet. Cook, stirring constantly, until sauce is thickened, about 30 seconds.

Transfer to platter, sprinkle with scallions, and serve.