Preheat oven to 400 degrees F (200 degrees C). Place tomatoes, eggplant, onion and garlic on a baking sheet and brush with oil.
Roast in preheated oven until very tender and brown in spots, 45 minutes.
Scoop out eggplant pulp and discard skin. Place eggplant pulp, tomatoes, onion and garlic in a large heavy saucepan with thyme and chicken broth. Bring to a boil over medium heat, then reduce heat and simmer until onion is very tender, 45 minutes.
Puree in batches in a food processor or blender, or using an immersion blender. Return to low heat and stir in cream. Bring to a simmer, thinning with more broth, if necessary. Season with salt and pepper. Ladle into bowls and sprinkle with goat cheese.