Combine the steak marinade ingredients in a ziplock bag and add the steak. Marinate in the refrigerator for 20 minutes, turning occasionally.
In a large bowl, whisk together the lime juice, vinegar, sugar, ginger, fish sauce chili sauce and garlic. Add the cabbage, carrots, green onions and cilantro. Toss to combine.
Remove steak from fridge and let it rest while you preheat grill or broiler. Place steak on a grill rack coated with cooking spray. Cook 5 minutes on each side or until desired degree of doneness. Let rest for 5 minutes.
Warm tortillas either by wrapping in foil and placing on the grill for about 2 minutes or microwave with a damp towel for about 30 seconds.
Cut steak on the diagonal across the grain into thin slices. Divide steak evenly among the tortillas and top with slaw.
Store your ginger in the freezer and use a grater/zester to mince the ginger!