Recipes that call for coconut milk usually refer to the canned variant ... coconut milk with water to add it to your cereal or drinks. Just sweeten it according to your taste.

In a small saucepan just big enough to hold the chicken with an inch of space at the top, combine chicken stock, coconut milk, lime juice, ginger and shallots. Bring to a boil over high heat.

Stir in ginger, chiles and remaining turmeric. Sauté until aromatic, about 1 minute. Pour in coconut milk and coconut cream, and simmer until flavors meld, about 5 minutes. Season with salt.