This dish contrasts warm and cold sensations, along with firm, soft, and crunchy textures. The tofu is pressed before grilling so that it becomes firmer. Because they're more flexible, the top halves of lettuce leaves make better wrappers than the bottom halves.
Cut tofu crosswise into 12 (1/2-inch) slices. Place tofu slices on several layers of heavy-duty paper towels. Cover tofu with additional paper towels. Place a cutting board on top of tofu; place a cast-iron skillet on top of cutting board. Let stand 30 minutes to 1 hour. (Tofu is ready when a slice bends easily without tearing or crumbling.) Arrange tofu in a single layer in a 13 x 9-inch baking dish.
Combine juice and the next 6 ingredients (juice through garlic) in a small saucepan, and bring to a boil. Cook 1 minute, stirring until honey dissolves. Pour over tofu. Cover and let stand at room temperature 1 hour.
Remove tofu from dish, and reserve marinade. Coat tofu with cooking spray. Place tofu on grill rack coated with cooking spray. Grill 3 minutes on each side or until browned.
Remove 12 large outer leaves from lettuce head; reserve remaining lettuce for another use. Remove bottom half of each lettuce leaf; reserve for another use. Place 1 tofu slice on each lettuce leaf top. Top each leaf top with 2 teaspoons cilantro, 3/4 teaspoon peanuts, 3 mint leaves, 3 carrot strips, and 1 basil leaf. Wrap leaf around toppings. Serve with reserved marinade.