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Prick eggplants all over with a fork. Thread garlic cloves onto a skewer. Grill the eggplants, turning occasionally, until charred and tender, 10 to 12 minutes. Grill the garlic, turning once, until charred and tender, 6 to 8 minutes.
Transfer the eggplants and garlic to a cutting board. When cool enough to handle, peel both. Transfer to a food processor. Add lemon juice, tahini and salt; process until almost smooth. Drizzle with oil and sprinkle with sumac, if desired.
Make Ahead Tip: Cover and refrigerate for up to 3 days.
Tahini is a thick paste of ground sesame seeds. Look for it in large supermarkets in the Middle Eastern section or near other nut butters.
The tart berries of a particular variety of sumac bush add a distinctive element to many Middle Eastern dishes. Find them whole or ground in Middle Eastern markets or online at kalustyans.com or buylebanese.com.