For the chicken: Combine the olive oil, sumac, salt, granulated garlic, pepper and lemon zest and juice in a large shallow dish or a resealable plastic bag. Add chicken thighs and mix to coat with the marinade. Refrigerate at least 30 minutes or up to overnight.
For the eggplant and naan: Use a paring knife to make crosshatch marks on the flesh side of each eggplant half. Drizzle both sides of the eggplant with oil and sprinkle with sumac, salt and pepper.
Preheat a grill for cooking over direct and indirect medium-high heat. Remove chicken from marinade and grill, flipping once, until cooked through, 5 to 7 minutes on each side.
Meanwhile, grill the eggplant, starting flesh-side down, for 5 minutes. Flip and cook 5 minutes more, then move to indirect heat to cook until tender, an 5 additional minutes.
Turn one of the burners to high heat. Lightly brush both sides of naan bread with olive oil and grill over high heat, flipping frequently, until slightly charred and warmed through, 3 to 5 minutes total.
For the yogurt tahini sauce: Whisk together the yogurt, tahini, parsley, honey, olive oil, cumin and lemon juice in a bowl, then season with salt and pepper.
Arrange chicken and eggplant on a platter. Drizzle with honey and olive oil. Top with fresh mint and parsley leaves. Serve with yogurt tahini sauce and grilled naan bread on the side.