Preheat oven to 325 degrees F. Place tomatoes in a large baking dish and drizzle with 2 tablespoons of the olive oil and sprinkle with the garlic, season with salt and pepper. Roast for 25 to 30 minutes, or until the tomatoes are soft.
Heat the remaining olive oil in a medium stock pot over medium heat. Add the onions and carrots and cook until the onions are soft, about 5 minutes. Add the roasted tomatoes, garlic, and the juices that have accumulated. Add the stock and fresh thyme and cook for 20 minutes. Place the cream in a small saucepan over medium high heat and cook until reduced by half. Transfer the mixture to a blender and blend until smooth, strain into a clean saucepan over low heat, add the reduced cream, and cook for 5 minutes.
For the Grilled Fontina-Mushroom Sandwich: Heat olive oil in a large saute pan, add the mushrooms, and cook until golden brown. Season with salt and pepper, and stir in the sage. Brush the bread on 1 side with the butter. Turn 4 of the slices over on a work surface. Divide the cheese among the slices then divide the mushrooms on top of the cheese. Cover with the remaining 4 slices of bread, butter-side up.
Heat a frying pan over medium heat. Add the sandwiches and cook, turning once, until golden, about 2 minutes per side.