How to Make It
Heat the oil in a large saucepan over medium-high heat. Add the onions and garlic and cook, stirring often, until softened, 5 to 7 minutes. Add the tomatoes (with their juices), broth, thyme, and ½ teaspoon each salt and pepper. Simmer, stirring occasionally, until slightly thickened, 15 to 20 minutes. Working in batches, in a blender, puree the mixture until smooth.
Meanwhile, in a small bowl, stir together the sour cream and horseradish. Form sandwiches with the bread, roast beef, Cheddar, arugula, and half the horseradish mixture. Heat a lightly oiled grill pan over medium heat and cook the sandwiches until the cheese is melted, 5 to 6 minutes per side. Top the soup with the remaining horseradish mixture and serve with the sandwiches.