Boil rice for a side dish in water until cooked, according to the instructions on the package.
In a medium bowl, combine the soy sauce, cornstarch, and horseradish. Put the chopped meat in this marinade, mix well.
Heat the oil in a large skillet over high heat. Put the meat in a preheated pan (do not remove the marinade). Fry the meat, stirring occasionally, until brown on all sides, about 2 minutes.
Transfer the meat to a plate, and put broccoli, onions, carrots in a pan, and cover with water and sesame oil. Cook for about 4 minutes, until broccoli is half cooked.
Pour the reserved marinade into a skillet, cook for about 1 minute, then add the grilled meat and cook the beef with broccoli for about 1 minute.
Sprinkle the cooked beef with broccoli with green onions and serve immediately with the steamed rice.