In a small saucepan, dissolve 2 tablespoons sugar in the vinegar over low heat. Stir in the ginger and garlic. Transfer to a bowl and add 2 tablespoons tamari and 1/2 teaspoon cumin. Let stand for 2 minutes, then discard the ginger and garlic. Add the cabbage, bell peppers and jalapeno; toss.
Preheat a grill or grill pan to high. Season the steak with grill seasoning. In a shallow dish, combine the remaining 1/4 cup tamari, 2 tablespoons sugar, 1 1/2 teaspoons cumin, the EVOO and lime juice. Add the steak, turn and let marinate for 10 minutes.
Grill the steak, turning twice, about 12 minutes for medium-rare. Let rest for 5 minutes, then thinly slice against the grain and serve with the slaw.