Place the cubed eggplant in a colander and sprinkle it with about 1 tablespoon of coarse salt. Let it sit for 30 minutes. Rinse thoroughly, gently squeeze out the excess water, and dry the eggplant with a clean towel.
Preheat the oven to 400°F (200°C).
Place the eggplant in a large bowl and drizzle with 1/3 cup olive oil. Toss thoroughly until the pieces are evenly coated.
Transfer the eggplant to an ovenproof casserole dish, keeping the pieces close together in a single layer. Pour about 1/4 cup warm water into one corner of the dish and gently tilt it to distribute the water underneath the eggplant.
Cover the dish with foil and roast for 10 minutes. Reduce the oven temperature to 350°F (180°C) and continue roasting for about 15 minutes, or until the eggplant is tender. Add hot water 2 tablespoons at a time if the dish becomes too dry.
Meanwhile, heat the remaining olive oil in a pan. Add the chopped onion and sauté for about 4 minutes, until softened.
Add the garlic and cook for another minute. Stir in the tomatoes, sugar, parsley, black pepper, and salt as needed. Simmer for 5 to 10 minutes.
Remove the eggplant from the oven. Add the tomato sauce and gently mix until the eggplant is evenly coated.
Return the dish to the oven and bake for about 10 more minutes.
Remove from the oven and allow the eggplant to cool and rest. Serve at room temperature with a generous spoonful of Greek yogurt and fresh parsley.
