1. Preheat oven to 400°F. Arrange tomatoes, eggplant, onion and garlic on a large baking sheet. Brush or drizzle vegetables with oil then roast them for 20 minutes.
2. Remove the garlic cloves and return the baking sheet to the oven for another 25 minutes, until the remaining vegetables are tender and brown in spots. Note: The original recipe had you keep them in the whole time, and mine, sadly, burned.
3. Remove sheet from oven and scoop eggplant from skin into a heavy, large saucepan or soup pot. Add the rest of the vegetables, the thyme and the chicken or vegetable stock and bring to a boil, then reduce to a simmer. Cook until onion is very tender, about 45 minutes (mine took longer). Cool slightly.
4. Working in batches, puree soup in blender until it is as smooth as you'd like it to be. (Or, if you have an immersion blender, you can do this in the pot.) Back in the pot, add the cream and bring the soup back to a simmer. Season with salt and pepper. Serve in four bowls, sprinkled with goat cheese.