One of my favorite things (easy too) to do with eggplant is to cut it up along with zucchini, summer squash, and onion... throw in frying pan, high heat until veggies start to soften & brown just a bit, then add a jar of Vodka Marinara (Trader Joe's has an especially good one) and simmer until veggies are done. Leftover cooked chicken is a good addition if you're looking for protein. I don't bother peeling the eggplant, although I might if it was particularly bitter or tough. Good over pasta or rice.
