DO-AHEAD TIP: Marinade steaks overnight or for at least 4 hours (see recipe). Prepare brown rice in time for dinner.
Place steaks in a large zipper-topped plastic bag. In a small bowl, whisk together remaining ingredients except for rice.
Blend well then pour mixture over the steaks. Seal the bag and gently massage the marinade into the steaks.
Refrigerate overnight or for at least 4 hours.
At the time of cooking, preheat an outdoor grill to MEDIUM-HIGH. Remove steaks from marinade. Grill for 4 to 7 minutes per side or until they reach desired level of doneness.
Allow steaks to rest for 10 minutes then thinly slice across the grain (diagonally) and serve over hot rice.