In a large bowl, mix the tamari, honey, sesame oil, mirin, vinegar, and arrowroot. Whisk this until smooth. Add the garlic, ginger, and cayenne. Divide the sauce in half, reserving some for cooking.
Slice the steak against the grain into 2 to 3 inch pieces that are not thicker than 1/4 inch. Place the beef in the bowl with 1/2 of the marinade and put to the side.
Make your rice while the beef is marinating. (See below).
Fill a wok or large skillet with enough water to submerge the broccoli. Bring this to a boil and drop the broccoli in. Boil for 2 minutes. Drain the broccoli in a colander and rinse under icy cold water to stop the cooking.
Return the wok to the burner over medium-high heat. Add 1 tsp of oil to the wok and sear 1/2 of the beef for 1-1/2 minutes, turning once. Remove this to a plate and repeat the process with the rest of the beef.
Place the remaining tsp of oil in the wok and add the broccoli. Stir for 30 seconds. Add the remaining sauce. As soon as it comes to a boil, add the beef and wait for the sauce to thicken. This will take approximately 1-1/2 minutes.
Serve the broccoli and beef over rice with sesame seeds sprinkled on top.