Prepare a hot direct fire for grilling.
Place the eggplant on the grill and cook until fork tender, turning once or twice. Remove the eggplant from the grill and cut each in half. Scoop the eggplant pulp into a bowl and discard the skin. Allow the eggplant to return to room temperature, then mash with fork or whisk. Set aside.
Combine tahini, garlic, lemon juice, cumin, salt and 1 Tbsp olive oil in a food processor. Blend until smooth, making sure to break up the tahini paste and roasted garlic. Add additional olive oil as needed until smooth. Add the mashed eggplant to the tahini mixture and blend to achieve the desired consistency. Taste for seasoning and add tahini, lemon juice or salt, if desired.
Transfer the dip to a serving dish. Drizzle the surface lightly with olive oil and garnish with a sprinkle of smoked paprika. Serve as a dip with an edible vegetable centerpiece, pita bread, crackers or chips. If you prefer a cold dip, chill in the refrigerator prior to garnish. Store refrigerated in an airtight container for up to one week.