Remove the cap, peel the eggplant, and cut into 1 1/2-inch cubes. Salt the cubes in a colander set over a bowl and let stand about 1 hour.

Rinse small batches of eggplant under cold water, then squeeze dry in a towel. Spread out on a clean towel and repeat until all cubes are done.

Fry the eggplant in vegetable oil about 1/2 inch deep over medium-high heat, in batches if needed. As soon as the pieces feel tender, lift out and drain on a rack or paper towels.

Pour off the oil and wipe the pan clean. Add olive oil and onion over medium-high heat and saute until light gold, then add garlic and stir just a few seconds.

Add the tomato strips, raise heat to high, and cook 8 to 10 minutes, stirring frequently, until the oil floats free from the tomato.

Add the eggplant and a few grindings of pepper, stir, and lower heat to medium. Cook 1 to 2 minutes, stirring once or twice. Taste and correct for salt.

Toss pasta with the sauce, then add Romano, ricotta, and basil. Toss again and serve at once, with grated Parmigiano-Reggiano on the side.