Poach the chicken: Place whole chicken in stock pot and cover with cold water. Add the seasonings and vegetables and bring to a boil. Lower to a simmer and cook 30 minutes. Strain and reserve broth for some other use. Remove the skin and discard. Remove meat in slices. Set aside.
Broil chicken livers on a rack under high heat, turning when light brown. Rinse under cold running water and pat dry.
Pour can of chicken broth in a saucepan with 1/4 cup cold water and bring to a boil. Remove from heat and mix in the gelatin. Cool to room temperature (should remain liquid).
Chop enough romaine lettuce to make 2 cups. Reserve rest for presentation.
Poach vegetables: In a small saucepan, bring cold salted water to a boil. Poach the celery 3 minutes; remove celery and poach carrot 2 minutes; remove carrot and poach squash 10 seconds. Refresh vegetables under cold running water and set aside. Assembly: Dividing ingredients equally among 4 serving dishes (4-5" in diameter, 1 1/2-2" deep), layer the ingredients as follows: First layer is a mixture of vegetables and lettuce, covering bottom of dish. Place one apple slice and some parsley on top, and one chicken liver in center of each dish. Next layer is slices of chicken, followed by layer of vegetables, parsley, and lastly chicken. Pour gelatin over ingredients and refrigerate, covered in plastic wrap, for at least 6 hours (or as long as 2 days), before serving so gelatin can set.
To serve, unmold and garnish with walnuts, remaining apple slices, whole romaine lettuce leaves and parsley.