BAKED EGGPLANT OMELET (FROCIA 'I MULINCIANI)

Steps:

• Peel eggplant and cut lengthwise into 1/8-inch-thick slices. Sprinkle sea salt over slices and arrange in 2 even stacks in a shallow dish. Put a flat dish on top of eggplant and weight with 1-lb can 2 hours.
• Rinse salt from eggplant under running water and pat slices dry between double layers of paper towel.
• Preheat oven to 350°F. Heat oil in an ovenproof 12-inch heavy skillet over moderately high heat. Sauté eggplant in batches of 3 or 4 slices until golden, about 2 minutes per side. Drain as sautéed on brown paper or paper towels.
• Pour off oil from skillet and wipe, leaving a light coating. Cover bottom of skillet with half of eggplant, overlapping slightly, and make another layer with remaining eggplant. Whisk together eggs and cheese in a bowl and stir together tomato paste and water in another bowl.
• Heat skillet with eggplant over moderate heat until hot and pour in egg mixture, lifting edges of eggplant so eggs coat bottom of skillet. Cook omelet, uncovered, over low heat, until eggs begin to set around edge, 5 to 7 minutes. Slowly pour tomato mixture in a spiral pattern over surface of omelet, then bake in upper third of oven until eggs are set and pale golden, about 20 minutes.
• Loosen side and bottom of omelet and slide onto a plate. Serve at room temperature with a few grindings of black pepper.