Eggplant with Buttermilk Sauce

Ingredients

• 2 large eggplants
• 1/3 cup olive oil
• 1 1/2 tsp thyme leaves, plus whole sprigs for garnish
• Sea salt and black pepper
• 1 pomegranate
• 1 tsp za'atar, marjoram or oregano
• 9 tbsp buttermilk
• 1/2 cup greek yogurt
• 1 1/2 tbsp olive oil, plus drizzle to finish
• 1 small garlic clove, crushed
• pinch of salt