Chicken Noodle Soup

1/2 tsp. kosher salt, plus more to taste

2 eggs, plus

1 yolk

8 cups chicken stock

2 tsp. dried sage

1 1/2 tsp. dried thyme

1 1/2 tsp. fennel seeds

5 whole black peppercorns

4 cloves garlic, minced

3 ribs celery, cut into 2 carrots, peeled and cut into 2¡å pieces

1 large onion, chopped

1 dried bay leaf

1 3 1/2-lb. chicken, cut into 8 pieces

2 tbsp. minced flat-leaf parsley

Freshly ground black pepper, to taste