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To make the soup, set a 4-quart pot or Dutch oven over medium heat. Add the olive oil, and when hot and shimmering, the onions and chili paste or red pepper flakes. Add a pinch of salt. Stirring often, saute until onions are very tender, about 10 minutes. Add the garlic and cook 1 minute more. Add the canned tomatoes, broth, and 3 sprigs thyme. Bring to a boil and then simmer for 20 minutes.
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Working carefully in batches with a regular or immersion blender, blend the soup until smooth and velvety. Return soup to the pot. Add salt and pepper to taste. Swirl in the cream and warm over low heat. (Soup can sputter and bubble, so place a lid slightly askew if needed.)
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Meanwhile, to make the grilled cheese, heat a skillet over medium-low/medium heat. Let the skillet get nice and hot. Spread about 1/2 tablespoon butter on one side of 4 slices of bread. Working quickly, add a small knob of butter and sprinkle a tablespoon of Parmesan in two places on the pan, then top with a slice of bread, butter side down. Add 1/2 cup grated Comte, Gruyere, or cheddar, and then another slice of bread butter side up. Cook 3 - 4 minutes. Use a spatula to scrape up any cheese and pick up the sandwich. Add another small knob of butter and another tablespoon Parmesan to the pan. Set the uncooked side, butter side down on top. Cook 3 - 4 minutes more.
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Repeat for the next two sandwiches.
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Slice cooled grilled cheese into 1-inch strips. Ladle soup into bowls, garnish with remaining thyme leaves, and serve with grilled cheese soldiers alongside.