Preheat grill. Brush flesh of the eggplant with olive oil and season with salt and pepper to taste. Grill flesh-side down for 15 to 20 minutes, turn over and grill an additional 15 minutes, or until soft. Let cool slightly and remove the flesh with a large spoon and mince..
In a large bowl, mix the tahini, garlic, shallot, lemon juice, olive oil, salt, pepper, cayenne, cilantro together until combined. Fold in the eggplant and reseason with salt and pepper and more lemon juice if necessary.
Brush naan with olive oil on both sides and grill for 1 to 2 minutes on each side. Cut into chunks.