Corned Beef and Cabbage Soup

Name: Corned Beef and Cabbage Soup
Ingredients: 1 medium onion, quartered; 3 stalks celery, quartered; 3 medium carrots, quartered; 3 tablespoons unsalted butter; Heaping 1/4 teaspoon ground allspice; 1 pound plum tomatoes, halved; 3 cups low-sodium beef broth; 4 cups chopped green cabbage (about 1/4 medium head); 1/2 pound Yukon gold potatoes, chopped; 3/4 cup quick-cooking barley; 1/4 pound corned beef, cut into thin strips (use leftovers or deli meat); Kosher salt and freshly ground pepper