Pungent turmeric, a cousin to ginger, is anti-inflammatory and may help ward off some types of cancer.
Preheat grill to medium-high (about 450°F). Stir together yogurt, olive oil, turmeric, garlic, lemon zest and juice and 1 tablespoon water in a small bowl. Stir in 1/2 teaspoon each of the salt and black pepper.
Cut eggplant lengthwise into quarters. Brush bell pepper, zucchini, yellow squash and eggplant with grapeseed oil.
Generously oil grill grate with grapeseed oil. Grill eggplant, zucchini and yellow squash, turning once, for 10 minutes. Grill bell pepper, turning occasionally, for 5 minutes. Cut eggplant diagonally into 1-inch-thick slices. Transfer grilled vegetables to a platter and sprinkle with remaining 1/2 teaspoon each salt and black pepper. Drizzle with sauce and sprinkle with pomegranate arils and mint.