1 (4- to 5-pound) corned beef brisket roast, rinsed, fat trimmed to 1/4 inch thick
4 cups low-sodium chicken broth
4 cups water
12 carrots, peeled (3 chopped, 9 halved crosswise)
2 celery ribs, chopped
1 onion, peeled and quartered
3 bay leaves
1 tablespoon whole black peppercorns
1 tablespoon minced fresh thyme
1 teaspoon whole allspice
3 tablespoons unsalted butter
1 1/2 pounds small red potatoes
1 head green cabbage (2 pounds), cut into 8 (2-inch) wedges
Pepper