Heat oven to 400° F. Rub the eggplant with 1 tablespoon of the olive oil. Roast, in a baking dish, until very tender, 40 to 45 minutes. Let cool.
Halve the eggplant and scoop the flesh into a medium bowl; discard the skin. Add the Feta, parsley, lemon, tahini, the remaining 2 tablespoons of oil, and ½ teaspoon each salt and pepper and toss to combine. Sprinkle with the additional parsley. Serve with the pita chips.