Wash the greens well and trim and discard any tough stems.

Bring a very large pot of water to a boil and add 2 to 3 teaspoons salt. (A large quantity of water is the key to avoiding bitterness.) Have ready a large bowl of iced water. Add the greens to the rapidly boiling water and cook 2 to 3 minutes, until tender but not mushy. Drain in a colander, shaking off excess water and then plunge the hot greens into the iced water. When the greens are cool, remove any ice from the surface and drain in a colander again. Then squeeze out any excess water and place in a bowl in the refrigerator.

Mix together the olive oil, lemon juice, salt and pepper. Toss with the cooked greens to coat thoroughly. Return to the refrigerator.

Cut the tomatoes into 1/2 to 3/4-inch slices. Arrange on 6 salad plates or a platter. Top the tomatoes with the cold dressed greens and garnish with shavings of Parmesan cheese. Serve cold or at room temperature.