In a food processor: puree peanuts, chiles, garlic, ginger, lime juice, fish sauce, oil, salt and sugar until smooth. Do not overmix as you can heat the mixture. Add the herbs and puree smooth. Check for seasoning. Oil shrimp on both sides and season. Grill on both sides for about 5 minutes total.
Place a layer of romaine on a plate. Lay 3 grilled shrimp on top and liberally drizzle with pesto.