Place in a deep dish; cover and let stand for 30 minutes.
Rinse with cold water; drain and dry on paper towels. In a 2-qt. saucepan, heat oil over medium heat
Add the tomatoes, garlic, basil and sugar; bring to a boil. Reduce heat and simmer, uncovered, for 45 minutes or until thickened, stirring occasionally.
Season with salt and pepper. Keep warm while preparing eggplant. In a large skillet, heat about 1/4 cup oil; brown eggplant, a quarter at a time, adding more oil as needed.
Place on a serving platter one row at a time. Cover with sauce and sprinkle with cheese.