To make the marinade, grate the zest from 1 lime; juice that lime. Whisk together 1/4 cup soy sauce, lime juice and zest, ginger and sesame oil. Chop 2 cloves garlic. With a mortar and pestle or with the flat side of a knife, mash the garlic into a paste. Whisk into the marinade.
Place the steak in a shallow dish and cover with the marinade, turning completely to coat. Cover the dish with plastic wrap and refrigerate for at least 1 hour and up to 12 hours. (Alternate method: place steak in a ziplock bag, pour over marinade, squeeze out air, seal and massage to distribute marinade.) Remove the steak from the refrigerator 30 minutes before cooking.
In the meantime in a food processor fitted with the large grating attachment, shred the carrots. Transfer to a large bowl. Add cabbage and cilantro; toss well. Cover tightly with plastic wrap and refrigerate for up to 3 hours.
To make the vinaigrette, juice the remaining lime. In a small bowl, whisk together the remaining 2 tablespoons soy sauce, vinegar, olive or peanut oil, fish sauce, lime juice and cayenne. Chop the remaining garlic clove. Using a mortar and pestle or with the back of a knife, mash garlic to a paste; whisk into the vinaigrette.
Heat a broiler or grill. Remove the steak from the marinade, scraping off excess; season with salt and pepper to taste. Cook, turning once halfway through, until browned, 5 or 6 minutes per side for medium/medium-rare. Transfer to a cutting board and let rest for 5 minutes. Thinly slice against the grain.
To assemble, add just enough of the vinaigrette to the salad to coat it; toss well. Taste and add more dressing or salt or lime juice if desired. Place the salad onto the center of a platter and top with the steak. Sprinkle with chopped peanuts and drizzle with more vinaigrette.