Preheat oven to 200 degrees C. Place tomatoes, eggplant, onion and garlic on a baking tray 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 stock. 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, blender or immersion blender. Return to low heat and stir in cream.
Bring to a simmer thinning with more stock, if necessary. Season with salt and pepper. Ladle into bowls and sprinkle with goats cheese.