Cut eggplants lengthways into 1cm slices; place in colander, sprinkle with salt, stand 30 minutes. Rinse; drain, pat dry. Cook in heated oiled large saucepan until browned.
Cook onion and half the garlic in same pan, stirring, until onion softens. Stir in tomato, paste and basil; simmer, uncovered, about 20 minutes or until thickened slightly. Blend or process tomato mixture until just combined.
Melt butter in same pan, add leek and remaining garlic; cook, stirring, until leek is soft. Add sugar; cook, stirring, about 5 minutes or until leek is browned lightly.
Preheat oven to 200°C/180°C fan forced. Oil deep 19cm-square (10-cup) ovenproof dish.
Position one pasta sheet in base of dish; top with a quarter of the eggplant, a quarter of the leek mixture, a quarter of the tomato mixture and a quarter of the cheese. Repeat layers three times, ending with cheese. Bake, uncovered, 50 minutes.