In a large saucepan, melt the butter in the olive oil. Add the onion and garlic and cook over moderately high heat, stirring until softened, about 4 minutes. Add the sun-dried tomatoes, diced tomato, stock and thyme. Season with salt and pepper; bring to a boil. Cover and simmer over low heat until the vegetables are very soft, 20 minutes. Discard the thyme sprigs.
Preheat a panini press. Transfer the soup to a blender, add the cream and puree until smooth. Return the soup to the saucepan and season with salt and pepper. Keep the sun-dried tomato soup warm over moderate heat.
Fill the ciabatta rolls with the sliced cheese and press until the bread is crispy and the cheese is melted. Serve the soup with the cheese panini on the side.