Heat vegetable oil in a large skillet over high heat until hot but not smoking. Add beef, and sprinkle with the salt. Cook, stirring occasionally, until browned, 3 to 4 minutes. Using a slotted spoon, transfer beef to a plate.
Add scallions and garlic to skillet. Cook, stirring constantly, until golden, about 30 seconds. Add broccoli and 1/2 cup water. Cook, stirring occasionally, until mixture is dry, about 3 minutes. Stir together broth, soy sauce, and cornstarch in a small bowl, and add to skillet. Cook, stirring constantly, until mixture is no longer cloudy, 1 to 2 minutes. Return beef and any juices to pan; cook, stirring often, until beef is heated through, about 1 minute. Remove from heat, and stir in sesame oil. Serve with rice.