Heat oil in large nonstick skillet on medium heat. Add eggplant, onions and garlic; cook 15 min. or until eggplant is very tender, stirring occasionally. Remove from heat. Stir in pasta sauce.
Combine ricotta, 1 cup mozzarella and 1/4 cup Parmesan.
Layer 1/3 each of the noodles, cheese mixture and pasta sauce mixture in 13x9-inch baking dish sprayed with cooking spray; repeat layers twice. Top with remaining mozzarella and Parmesan.
Bake 40 to 45 min. or until heated through. Let stand 10 min. before cutting to serve.