Toss the Jerusalem artichokes and butternut pumpkin in 2 teaspoons olive oil and place in a roasting tin. Roast until browned and tender.
Bring a saucepan of water to the boil. Add the green beans and blanch until tender but still crisp, 2-3 minutes. Remove with tongs and blanch with cold water. Set aside.
Add the potatoes to the boiling water and boil until tender, about 10 minutes.
Heat a ribbed griddle pan until very hot. When the potatoes are cooked, peel and slice them. Rub a little oil on the slices and char-grill.
Just before serving, toss the cooked vegetables, olives and tomatoes with the Parmesan. Arrange on a large plate and season with salt and pepper. Drizzle with truffle oil and balsamic. Top with quartered eggs and a sprinkling of lemon juice.