Preheat the grill. In a mixing bowl, combine the extra virgin olive oil and lemon juice together. Whisk in the herbs until incorporated, reserve 1/4 cup of the vinaigrette. Season with salt and pepper. Place the asparagus in a 8 by 8 by 1 1/2-inch square glass dish. Pour the herb vinaigrette over the asparagus and let marinate for 30 minutes. Brush each fourth of the radicchio with the olive oil and season with salt and pepper. Place on the grill, core side down, and grill 1 to 2 minutes on each side. Remove from the grill and set aside. Toss the crab meat with the reserved vinaigrette and season with salt and pepper. Fan out the leaves of the radicchio and stuff the crab meat in between the leaves. Remove the asparagus from the vinaigrette and reserve the vinaigrette. On an over-sized platter, arrange the asparagus on the bottom. Place the radicchio over the asparagus. Drizzle the entire platter with some of the reserved vinaigrette. Garnish with parsley and Parmigiano-Reggiano cheese.
Yield: 4 servings