Using a mortar and pestle, pound half of the galangal with the garlic into a paste. One at a time, add the cilantro stems and roots, miced lemongrass, ground peppercorns, and shallots in sequence, adding each new ingredient only after the previous one is pureed and incorporated into a fine paste. Set aside, or transfer to a jar with a tight-fitting lid and refrigerate.
In a 4-quart saucepan, bring the coconut cream and milk to a gentle boil over medium heat. Do not overheat or it will curdle. Add the galangal paste and stir well, then add the chicken and bring to a boil. Add the kaffir lime leaves, lemongrass stalks, sea salt, fish sauce, the remaining galangal and the chiles, cover, and simmer over medium-low heat for about 45 minutes, until the chicken is completely cooked.
Transfer to a serving bowl, garnish with the cilantro sprigs, and serve with the lime wedges.
Courtesy Su-Mei Yu's Cracking the Coconut (Morrow, 2000)