Heat grill to medium-high or crank oven to 375ºF.
Using a fork, pierce some holes in the skin of the eggplant (to avoid explosion) and grill over indirect heat, turning every 7 minutes, until the skin is blackened and the body is nice and soft, about 30 minutes total. If you do not have a grill, roast your eggplant for about 30 minutes.
Remove eggplant from heat, wrap in plastic wrap, and let cool 1 hour.
Cut off the stem end of the plant and squeeze out the flesh. Place the eggplant flesh in a colander and drain for 30 minutes.
In a food processor, combine the drained eggplant, garlic, lemon juice, tahini, and salt. Process 10 to 15 seconds to combine. Add the parsley and pulse 2 to 3 times to combine. Taste and add black pepper, if desired. Serve with pita chips.