Rinse all of the vegetables well, including the kombu.
In a 12-quart or larger stockpot, combine the carrots, onions, leek, celery, red potatoes, sweet potatoes, yam, garlic, parsley, kombu, peppercorns, allspice berries and bay leaves. Add the water, cover and bring to a boil over high heat. Decrease the heat to low and simmer, partially covered, for at least 2 hours, or until the full richness of the vegetables can be tasted. As the broth simmers, some of the water will evaporate; add more if the vegetables begin to peek out.
Strain the broth through a large, coarse-mesh sieve (use a heatresistant container underneath), and discard the solids. Stir in the salt, adding more if desired. Let cool to room temperature before refrigerating or freezing. Store in the refrigerator for up to 5 days or in the freezer for up to 6 months.