Step 1

Pulse the onion, celery and carrots in a food processor until they are pea-size pieces.

Step 2

Melt the butter in a large pot over medium-high heat. Add the chopped onion, celery and carrots and the allspice and cook, stirring occasionally, until the vegetables are slightly softened, about 5 minutes.

Step 3

Add the tomatoes to the food processor and pulse until finely chopped. Transfer the tomatoes to the pot and add the beef broth, cabbage, potatoes, barley and 4 cups water; cover and bring to a boil. Uncover, reduce the heat to medium low and simmer until the potatoes and barley are tender, about 20 minutes.

Step 4

Stir in the corned beef and season with salt and pepper.