The key to making great baba ghanoush lies in not being afraid to char the bejesus out of the eggplants -- it gives the flesh a beautifully smoky flavor after you peel away the skin. You can do it directly on a gas burner, on a grill, or in a broiler. The skin should be completely black and the center of the eggplants thoroughly cooked before you call it a day. Just don't forget to tear open the shutters and throw up the sash (and turn on the exhaust fan) so the house won't smell too smoky. (Very special note here: the Amazon link below is an affiliate link. But also, those tongs -- which I use daily in the Umami Girl kitchen -- are being sold on Amazon by Cope because he does awesome stuff like that from time to time.)
To char the eggplants, either set them directly on a lit gas burner or grill, or place in the oven a few inches below the heat source with the broiler on high. Allow the skin to turn completely black and flaky on the first side, then turn the eggplants with long-handled tongs to begin charring on the next side. Continue turning the eggplants every few minutes until all sides are charred. The process will take 10 to 15 minutes. You'll know you're done when all the skin is charred and the eggplants are soft all the way through to the middle. Expect some drips and minor flare-ups. It's worth it. (But please be careful.) Set eggplants on a plate to cool.
When eggplants are cool enough to handle, remove the stems and peel away and discard as much of the skin as possible. You want to get rid of most of it, but don't worry if there are little bits left on here and there.
Add the eggplant flesh, tahini, lemon juice, garlic, salt, cumin, and pepper to a food processor fitted with the blade. Pulse to blend thoroughly. (Alternatively, you can grate the garlic on a rasp and then just mash up all the ingredients in a bowl with a fork.) Taste and adjust seasoning.
Scrape baba ghanoush into a serving bowl, drizzle with olive oil and sprinkle with parsley. Serve with pita wedges or crackers.