Combine the coconut with the milk in a heavy saucepan. Heat slowly, bring to a simmer, then remove from the heat and cool. Strain the milk, pressing down on the coconut meat to extract all the liquid. Squeeze all the coconut through a towel to get any last drops. Discard the coconut.
Remove the grassy tops of the lemongrass, leaving stalks about 6 inches long, and cut off any hard root section. Using the blunt edge of a large knife or cleaver, bruise each stalk all over. Cut each stalk into 4 pieces.
In a saucepan bring chicken stock to a boil, reduce to a simmer, then add lemongrass, galanga, peppercorns, serrano chile, and lime leaves. Simmer 15 minutes, then add coconut milk and cook an additional 5 minutes. Add chicken pieces, straw mushrooms, snow peas, and carrots. Simmer for another 10 to 12 minutes. Stir in fish sauce, and lime juice and serve immediately. Garnish with cilantro leaves. Be careful to avoid chewing the lemongrass, galanga or ginger, or lime leaves when eating.
c.1997, M.S. Milliken & S. Feniger, all rights reserved