I was looking at the soup recipe, guessing the chicken flavor just comes through since there’s no chicken called for. I think you could boil the chicken for the loaf and use the stock for the soup, making sure you’ve got enough stock for the quart the soup calls for, plus 2C reduced stock for the loaf.

COLD CHICKEN AND PEA SOUP

6 servings

1 leek, cut into quarters lengthwise, washed thoroughly
½ head lettuce, washed well
2 Tbsp butter
1 quart chicken stock, hot
1½ C cooked peas
1 small bay leaf
1 whole clove
Salt, black pepper (preferably freshly ground), ground nutmeg, all to taste
¼ C heavy cream, whipped
1 Tbsp or more chives, chopped

Grind together leeks and lettuce in a food chopper using finest knife or blade. Heat butter, add leek-and-lettuce mixture, and sauté until soft but not browned. Add stock, peas, bay leaf, clove, and salt, black pepper, and nutmeg, and cook until peas are very tender. Strain stock, rub vegetables through a sieve or food mill, or purée in blender or food processor, combine with stock, and chill thoroughly. At serving time, fold in whipped cream and serve garnished with chives.

From The Beaufort Cook Book, A Treasury of Carolina Recipes, collected by Dee Hryharrow and Israel M. Hoogenboom (1965)

“Turn out on a small platter. Serve sliced.”

COLD CHICKEN LOAF

1 hen
Water
1 onion, quartered
½ C chopped celery
4 hard-boiled eggs, quartered or sliced
½ C chopped almonds
Salt, pepper, to taste

Place hen in a large pot with water, onion and salt and pepper and simmer until very tender. Remove meat from skin and bones, chop meat fine and mix with celery and almonds. Place a layer of chicken mixture in bottom of loaf pan, arrange hard-boiled eggs down center, place remaining chicken mixture around and over top. Reduce stock to 2 C by rapid boiling, check for seasoning, pour carefully over chicken until level with top of pan and chill.