How FORTUNATE you are to have such wonderful neighbors! Eggplant is both wonderful to eat and it is easy to prepare.
Pick the eggplant when it is dark purple -- and this likely to be when the vegetable is somewhere between 6" long and 10" long and 3" to 5" in diameter. You can search on the web for recipes by "Googling" eggplant.
Because I LOVE Italian food, my personal favorite is to serve it as a main dish Italian meal - Eggplant Parmesan. I'll give you my recipe/technique for that, below. I recommend trying that first, as it is one of the most common ways to prepare eggplant. Greek food is good, too, so I am giving you a link to Eggplant Moussaka. You do not indicate whether you "like" to cook or not, but I encourage you to experiment. Because you are likely to have a lot of it on hand for a couple of months, try several methods.
For variety, it can be prepared very simply by steaming it and serving it as a side vegetable. Wash and peel* the eggplant with a veggie peeler. Cut it into 1" chunks and steam it (using a steamer-basket placed in a saucepan, or steam it in the microwave). Then, serve it hot. You can drizzle melted butter over the whole bowl and season with salt and pepper (toss in garlic salt if you like). Or if you wish, everyone can individually melt pats of butter on it and season with salt and pepper to their own tastes (Molly McButter is a good alternative to the butter if you want it to be very low-cal.) Sometimes I steam large chunks of onion along with it. You can also top it with cheese sauce in the chunked form. Again, you can "Google" a cheese sauce recipe or for quick-and -easy, just melt Cheese-Whiz and spoon on the amount you like. I will give you a recipe for Eggplant casserole, too.
[* Note: I do not peel the eggplant when I slice it thin to make eggplant Parmesan. However, I do peel it when I chunk it to steam or sauté’ and eat like squash. When you peel it, it will begin to turn dark immediately. Just have some lemon juice, or Fruit Fresh (ascorbic acid) ready to sprinkle over it to minimize the darkening.]
Most of all, have fun and ENJOY! This should be great "food fun" for your 4-year old gardener.
Quick Eggplant Parmesan: Below is an official recipe that provides the basic process. But if you want a “quick” version, just slice the eggplant thin, dip slices in egg and roll in Italian breadcrumbs (or crushed crackers or cornflakes), sauté’ eggplant slices in a small amount of olive oil, then place them in a baking dish in alternating layers of (1) prepared Marinara Sauce (I think “Classic Tomato and Basil” is best; it can be purchased at Sam’s Club sold three (3) 1-quart jars per package) and (2) shredded mozzarella cheese (Also, Sam’s sells a 5-lb. bag of “Stella” brand shredded mozzarella that is very good; I keep it on hand.) Use plenty of sauce and cheese; pop in the oven and bake until bubbly! Yum!
Eggplant is breaded and fried then topped with sauce and cheese and baked, in this Eggplant Parmesan recipe.
1 large eggplant, about 1 1/2 pounds
2 eggs, beaten
1 1/2 cups fine, dry bread crumbs mixed with 1/2 teaspoon salt and 1/2 teaspoon ground black pepper
2 cans (8 ounces each) tomato sauce
1 teaspoon dried leaf basil
1/2 teaspoon dried leaf oregano, crumbled
16 ounces sliced mozzarella cheese
1/2 cup grated Parmesan cheese
Directions for Eggplant Parmesan
Wash eggplant and cut crosswise into 1/2-inch thick slices. Dip into beaten eggs then dredge with seasoned breadcrumbs. Place slices on a plate and chill for 30 to 45 minutes. Heat about 1/8-inch of oil in a heavy skillet. Fry eggplant on both sides until golden brown and crispy. Drain well on paper towels. In a saucepan, heat tomato sauce, basil, and oregano. Spread 1/3 of the sauce in a greased 12x8x2-inch baking dish. Layer half of the eggplant, half of the mozzarella cheese slices, another 1/3 of the sauce, and half the Parmesan. Repeat layers. Bake at 350° for 30 minutes, or until hot and bubbly.
Eggplant Parmesan serves 6.
For Greek Eggplant Moussaka:
Eggplant (or Squash) Casserole
1-2 Large Eggplant (or 6-7 Yellow "crookneck" squash)
2 eggs, beaten
8-10 saltine crackers, crumbled fine
1-2 Tbl. sugar (or more, to taste)
Salt & pepper, to taste
1 cup Velveeta cheese (or more, to taste)
1 Tbl. flour
Dice the eggplant* in 1/2" cubes and boil in a small amount of water (appx. 1 cup) until tender. Drain the excess water and cool slightly. While eggplant is cooling, crate the Velveta cheese (use a grater with large diameter grate. If you use a small amount of flour on the velveta chunk and on your hands, it will help you to grate it without it becoming sticky.) Using a fork, beat 2 eggs in a small bowl until well mixed. Place cooked eggplant in a large mixing bowl and mix in all ingredients, stirring vigorously with a wooden spoon. Pour into a shallow 2-quart baking dish and bake uncovered at 350 degrees for 45-60 minutes, until lightly browned.
* If you are using yellow squash for this dish, cut the squash into 1" to 2" cubes. Squash has greater water-content and will cook to tender more quickly than eggplant, so it needs to be in larger pieces when parboiling it.