Bring water with remaining 2 teaspoons salt and ginger to a boil in a 6-8 quart pot wide enough to hold chicken. Put chicken, breast down, in water and return to a boil, covered. Simmer the chicken, partially covered, 20 minutes and remove from heat. Let the chicken stand in hot broth, covered and undisturbed, until just cooked through, 15 to 20 minutes.