Slice the white portion of the leeks and place in a large stockpot; reserve the green tops. Add the carrots, celery, onions, and garlic to the pot. Using kitchen string, tie together the reserved green leek tops with the parsley and thyme sprigs and bay leaf. Add to the pot along with the water.
Place over medium-low heat and bring slowly to a simmer, regularly skimming off the scum tha