Preheat oven to 450°.
Remove white papery skin from garlic head (do not peel or separate the cloves); wrap in foil. Bake at 450° for 45 minutes, and cool 10 minutes. Separate cloves; squeeze to extract garlic pulp. Discard skins.
While garlic roasts, place eggplant, cut sides down, in a baking pan. Add water to a depth of 1/4 inch. Bake at 450° for 30 minutes or until tender, and cool 10 minutes.
Scrape pulp from eggplant skins; discard skins. Place eggplant, garlic pulp, sesame seeds, and remaining ingredients in a food processor; process until smooth, scraping sides of bowl.