Further to bella s.f. - if you do want cubes of eggplant for a dish, roasting works quite well. Coat the sheet pan with some olive oil and toss the chunks in it. Maybe 400 degrees or 425 for about 20 to 30 minutes. Keep an eye on them and stir them once or twice. They get a little caramelized and are great tossed in with pasta dishes.

I don't like to saute or fry eggplant because of all of the oil that it absorbs. I brish slices with oil and then roast them in the oven on a sheet pan, or cook them on a cast iron griddle. I have never tried to oven roast cubes of egglplant, but thinking about it now, I don't see why not. I will have to try that. I like to roast baby artichokes in the oven in olive oil with fresh thyme, slices of garlic, lemon sliices, white wine. and lemon juice. Salt and pepper of course. Artichokes can be pretty labor-intensive. I have been reading lately about frozen artichokes. They have been recommended quite a bit. The Trader Joes where we live, have bags of frozen baby artichokes. I have used them in a chicken dish, but not on their own. I, personally, do not care for the marinatd ones. I don't like the quality of them, taste-wise or texturally, but they are really very popular. When using fresh artichokes, most people cut off the stem. I cut off the very tip of the stem and peel the rest of it, still attached to the artichoke. I think the stems are wonderful. They are tender, just like the heart.

I'm guessing by your question about which parts of the artichoke are the "best" that you're an artichoke newbie. I'm also sure you know this, but just to be safe......the fuzzy choke inside the leaves, that's attached to the base (which is the heart) is not edible. You can remove it before cooking, if you've trimmed the 'choke down, or after, when you've pulled all the leaves off and scraped the bit of flesh from the bottom with your teeth. Also, again, sorry if you already know this but....the tips of the leaves have a sharp little thorn on them that hurts like the devil if it pricks your finger. Cut off the top 1/3 of the 'choke with a sharp, heavy knife, then cut the tops off the rest of the leaves with a pair of kitchen shears. Rub the cut surfaces with lemon to keep them from oxidizing.

As for the best.......depends on your taste. I love the flesh from the base of the leaves just as much as I love the hearts. But the heart is considered the "prime real estate" of the artichoke world.

For the eggplant, pasta alla norma is always delicious! Here's a basic recipe:
http://dinersjournal.blogs.nytimes.com/2009/04/21/pasta-alla-norma/- (eggplant parm is usually a crowd pleaser as well)

Did you buy whole, raw artichokes? or marinated hearts? or Jerusalem artichokes etc. If you have large raw artichokes, you might make some stuffed artichokes with homemade breadcrumbs which you sautee w garlic, oil, and herbs and then toss with some good grated parmesan cheese and then stuff into the trimmed artichokes and steam or simmer . . . You can serve with a garlic-oil dipping sauce as well--

Lately I have seen artichokes everywhere and I think, depending on what kind you have or want to use, you can really prepare them a million ways- crispy fried artichoke leaves with aioli sounds great to me, and then you can do something different with the hearts! Enjoy!