Place an 8- to 10-quart stove-top covered casserole on the burner and add the beef, beer, water, bay leaves, peppercorns, parsley, and salt.
Heat a frying pan and add the butter or olive oil. Saute the garlic, leeks, and yellow onion for a few minutes and add to the casserole. Cover the pot and simmer gently for 3-1/2 hours, or until the meat is very tender. (This will normally take about 1 hour per pound of brisket.) In the last 25 minutes of cooking, add the carrots and red potatoes. In the last 15 minutes of cooking, add the turnips, cabbage, salt and pepper.
If the vegetables are not done to your liking, cook them longer, but do not overcook. Remove the toothpicks from the cabbage before serving.