Preheat grill to 400° to 450° (high) heat. Stir together ginger, oil, and 2 Tbsp. cilantro in a small bowl. Rub cilantro mixture on steak. Sprinkle with salt and pepper.
Grill steak, covered with grill lid, 6 to 7 minutes on each side or to desired degree of doneness. Remove from grill; squeeze juice from lime over steak. Cover loosely with foil, and let stand 10 minutes.
Meanwhile, prepare rice according to package directions, and stir in edamame and remaining 4 Tbsp. cilantro. Cut steak across the grain into thin slices; serve over rice.