Preheat oven to 425 degrees. Place eggplant and garlic on a rimmed baking sheet and rub with 2 tablespoons oil. Roast until garlic is soft and golden, 20 minutes. Remove garlic and set aside. Continue to roast eggplant until soft and deflated, 20 to 25 minutes more. Let cool 20 minutes.
Slice eggplant open and scrape flesh into the bowl of a food processor. Peel garlic and add to bowl, along with lemon juice, tahini, salt, and 2 tablespoons oil. Process until smooth. (To store, refrigerate, up to 2 days.) Serve drizzled with more oil and a sprinkle of paprika if desired.
Refrigerate, up to 2 days.