Preheat the broiler. In a large bowl, combine the pork, cilantro, ginger, remaining 3 teaspoons soy sauce and 1 teaspoon garlic. Form 8 oval patties about 1/2-inch thick and broil, turning once, until cooked through, about 4 minutes per side. Spoon into lettuce cups and top with the carrots. Serve with the dipping sauce.