Wash and dry eggplants. Peel garlic and set aside. If the cloves are very large, cut in half. Make multiple 1/2-inch slits in the eggplant and stud with garlic. Push towards the center of the eggplant so the garlic is not sticking out. When done, coat eggplant with olive oil and sprinkle with salt.
Place in the center of the cooking grate until the eggplants have collapsed and are soft. You will need to turn occasionally. This will take approximately 30 minutes, depending on the size of the eggplants. When very soft, cut in half and scrape flesh and garlic from skin. Mash with a fork and mix in enough olive oil to make creamy. Season with salt, pepper and parsley. Serve with pita wedges or flatbread.