Choose nice, firm eggplant for this preparation. Cut lengthwise in 1/8 inch slices. Boil in plenty of water for 5 minutes. Drain well and pat both sides dry with a cotton or linen dish cloth.
Heat olive oil and butter in a medium-sized sauce pan over medium heat. Sauté chopped onion until slightly golden, add tomato sauce and eggplant.
Cook for 30 minutes, stirring occasionally and adding broth, if necessary, until eggplant is soft and completely cooked. Sprinkle with grated Parmigiano Reggiano. Serve immediately or at room temperature.