Chop carrots, onions, celery and leeks into 1- to 2-inch chunks; leave the potatoes whole. Combine the vegetables with the remaining ingredients in a soup pot or stock pot. Bring to a boil. Reduce heat to maintain a simmer and simmer for 1 hour. Strain the broth through a colander, then once more through a fine sieve. If the broth tastes weak, pour it back into the pot and simmer until reduced to a flavor you prefer, 20 to 30 minutes more.