Combine ham shanks and cold water in a 4- to 5-quart heavy pot and bring to a boil, skimming any foam. Add remaining ingredients and simmer, partially covered, until shanks are tender, about 2 hours. Pour stock through a fine-mesh sieve into a large metal bowl, reserving shanks and discarding remaining solids. Discard skin and bones from shanks. Trim and coarsely shred meat, then return to stock.