Step 1: Preheat oven to 400 degrees F (200 degrees C). Grease a 10x14x2-inch baking pan.

Step 2: Heat margarine in a skillet over medium heat; stir in onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to low and continue to cook and stir until onion is very tender and dark brown, about 40 minutes more.

Step 3: Bring chicken broth to a boil in a large pot; stir in chicken breasts, reduce heat, and simmer until chicken is no longer pink at the center, about 20 minutes. Remove from heat. Remove chicken breasts to a plate using a slotted spoon; reserve broth.

Step 4: Juice potatoes with an electric juicer; place dry potato flesh into a bowl and discard juice. Stir salt and pepper into potatoes; stir in enough reserved broth to make the mixture the consistency of oatmeal. Set remaining broth aside.

Step 5: Spread half of potato mixture evenly into the prepared pan. Lay cooked chicken breast evenly over potatoes; scatter caramelized onion evenly over chicken. Spread remaining potato mixture over onions and chicken to cover.

Step 6: Bake in the preheated oven until golden brown, about 1 hour. Reheat chicken broth; pour over individual servings as desired.