Preheat oven to 350°. Place eggplants on a well-oiled sheet pan and pierce lightly on all sides with a small knife. Bake until soft, about 30 minutes. (For an attractive smoky flavor that will add complexity to the finished dish, grill eggplants on a barbecue, blacken them over the gas burner on a stove, or sear them on a very hot, lightly oiled griddle, cooking until their skin wrinkles and takes on a bronze tone. If not cooked through, finish in a 350° oven for about 10 minutes.)
Allow eggplants to cool enough to handle, then cut them in half lengthwise and scoop out their flesh with a spoon. Set scooped-out portion aside to cool further. Discard the skin.
When eggplant has cooled sufficiently, place in a clean thin kitchen cloth or several thicknesses of cheesecloth, and squeeze to remove excess moisture and bitter juices. Set aside in a large sieve or colander to drain further.
Finely chop garlic, then crush it into a paste with 1 teaspoon salt. Place in a food processor, add tahineh and lemon juice, and process until mixture thickens, then thin again slightly with several tablespoons of room-temperature water.
Add the eggplant flesh and remaining olive oil to the food processor and pulse several times to make a thick, coarse purée. Season to taste with pepper, adding salt if necessary.
Serve in a bowl, garnished with parsley or coriander. If desired, sprinkle paprika across top of baba ghannouj in the form of an "X". Serve with pita chips. (Cut pita into wedges, brush with olive oil, salt to taste, then toast lightly in the oven.)