Toss eggplant with the thyme, garlic, olive oil and balsamic vinegar. Grill on both sides. Set aside.
In a soup pot, heat the 4 tablespoons of olive oil, add garlic and leeks. When lightly brown, add the stocks and grilled eggplant. Simmer 20 minutes. Puree in food processor. Add salt and pepper to taste.
To serve, place in bowls and top with sour cream and fresh thyme