Step 11 Heat the grill to high. Line a baking sheet with paper towels and set aside.
Step 22 Fill a stockpot or large, deep pot with water and bring to a rolling boil over high heat. Add the prawns head-first to the pot all at once and cover. Cook 30 seconds. Drain the prawns in a colander and rinse with cold water. Place the prawns on the baking sheet and pat dry with paper towels.
Step 3Cut the asparagus into 3-inch pieces. Blanch 30 seconds, then plunge into a bowl of ice water. Drain and set aside.
Step 4Blanch the tomato 30 seconds, then plunge into ice water. Remove the tomato, cut out the core and peel. Cut the tomato into quarters, seed and dice. Set aside.
Step 5Place the prawns in a large bowl. Add 1 tablespoon of the olive oil and salt and pepper to taste. Place the prawns on the grill, cover, and cook until the shells are slightly charred, 2 to 3 minutes. Turn them over and cook 2 to 3 minutes more, depending on the size. To check for doneness, remove a prawn from the grill and cut into the tail portion. The meat should be opaque and cooked through in the center. Remove the prawns from the grill and set aside.
Step 6Heat a large skillet over medium-low heat. Add the butter and melt; do not sizzle or brown. Add the ginger and cook until fragrant, 30 seconds. Add the asparagus and peas and warm gently, 1 minute. Increase the heat to medium and add the tomato. Cook, stirring gently, until the tomato breaks down slightly, 3 to 4 minutes. This will thicken the pan juices. Season with salt and pepper to taste and add the chives. Set aside.
Step 7Cut the prawns in half down the middle with a sharp knife and devein if necessary. Divide the prawns among 4 large warmed plates and spoon the asparagus mixture over and around them. Squeeze lemon juice over the prawns, drizzle liberally with the remaining 2 tablespoons of extra-virgin olive-oil, and sprinkle with the tarragon and a little fleur de sel.