I make something similar to jtluvsjl's recipe.
You shouldn't need to salt eggplants these days, so what I do is slice across about quarter to third inch thick, put into a plastic bag and drizzle in a bit of oil. Then shake the slices around to get oily - doesn't use as much as brushing - they are like sponges!
Then I griddle them [I use my electric machine] but you can bake or grill [that's broil in US, isn't it?] till softened.
Meanwhile, make a tasty thick tomato sauce. I use oil to soften onion and garlic, then add tinned chopped tomatoes, dash balsamic, pinch chilli flakes, couple sun dried tomatoes chopped, herbs eg oregano, basil, and salt and pepper - cook till thick.
Layer up the eggplant slices in an ovenproof dish with tomato sauce, putting a layer of torn-up mozzarella in the middle. Finish with a layer of eggplant, then sprinkle the top with freshly finely grated Parmesan. Spray lightly with oil and bake till bubbling.
Yum yum!!