In a large kettle, sear the beef brisket over medium heat until browned; pour off the fat.
Add the broth, onion, large carrot, celery, bay leaf, and garlic.
Cover, bring to a boil reduce heat, and simmer 1 1/2 hours.
Remove vegetables and bay leaf; reserve for gravy.
Add the remaining vegetables in order given: cauliflower, small carrots, and onions.
Sprinkle the cabbage with cayenne, then add to the pot.
Cover and simmer an additional 1 1/2 hours or until the meat is tender and the vegetables are cooked but not soggy.
Transfer to a serving platter.
For the gravy: mash the vegetables and bay leaf that was set aside earlier. Bring to a boil and reduce to desired consistency. Remove the bay leaf. Pour over the brisket when ready to serve.