POSITION a rack in top third of oven and preheat to 375F. Line a large baking sheet with parchment paper.
KEEPING them attached at the stem, slice eggplants vertically, 1/2 in. apart. Press each eggplant at the stem until the slices fan out, then brush with oil. Season with salt and pepper.
ARRANGE on sheet and bake, flipping halfway, until tender, about 30 min.
SUMAC-TAHINI sauce: Whisk yogurt, tahini, lemon juice, garlic, 1/2 tsp sumac and salt in a bowl. Slowly whisk in 1/3 cup water, plus 1 tbsp, until smooth. To serve, drizzle over eggplants. Top this eggplant recipe with pomegranate seeds, mint, pine nuts and remaining 1/2 tsp sumac.