Vinaigrette: Place all ingredients in a small bowl and whisk together. Season with salt and pepper to taste.
Salad: Toss the potatoes and asparagus in oil to thoroughly coat and season with salt and pepper. Place the potatoes, and asparagus on grill over medium heat. Cook the potatoes for 15 minutes, turning them 3 times as they cook. Cook the asparagus for 3 minutes. Remove from the heat and set aside. Place the tuna in a shallow dish and add 1/4 cup vinaigrette. Turn to coat evenly and then place on grill over medium heat. Cook for 2 minutes on each side. Remove from heat and cut the tuna across grain in 1/2-inch slices. Arrange radicchio and lettuce around a platter, building it up slightly in the center. Place eggs, beans, asparagus, and potatoes around the platter. Fan tuna slices across top of lettuce. Add tomatoes and olives. Garnish with eggs and parsley. Drizzle vinaigrette over the salad.