Preheat the oven to 350°F and adjust rack to middle position. Place the tomatoes on an oiled baking sheet in an even layer. (This should take up about half of the baking sheet). Evenly sprinkle the tomatoes with the whole cane sugar. Fill the rest of the baking sheet with the eggplant, onion, and garlic. Drizzle the ghee over the eggplant, onion and garlic (rub the oil into the vegetables with your hands) and season generously with salt and pepper. Roast for about 45 minutes, until tender. Remove the garlic pulp from the skins.

Place the vegetables and peeled garlic in a large stock pot and add the chicken broth and thyme. Bring the mixture to a boil and then reduce the heat to a simmer. Continue to simmer for 30 minutes until a knife can be inserted into the eggplant with little resistance. Puree the soup using a hand immersion blender or you can also blend until smooth in small batches in a blender. Stir cream into soup and season with salt and pepper if needed. Ladle into bowls and garnish with Parmesan cheese and fresh basil.