For the soup: Melt the butter in a large saucepot over medium heat. Add the garlic, celery, carrot and onion and sweat until translucent, about 8 minutes. Add the tomatoes, heavy cream, thyme and parsley along with just enough water to cover the vegetables. Simmer until tender, 30 to 45 minutes. In a blender, working in batches, puree the soup on high speed until it takes on a velvety texture, at least 2 minutes per batch. Add salt, pepper and vinegar to taste.
For the grilled cheese: Melt 1 tablespoon of the butter in a large saute pan over medium-low heat. Lay two slices of the bread in the pan and top each with a slice of the American cheese. Cook until the cheese is melted and the bread is golden and crispy. Make a sandwich of the two slices. Repeat the process with the remaining bread and cheese, adding more butter to the pan as needed. Cut the sandwiches in half and serve with bowls of the tomato soup.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.