Make the broth: Place the chicken into a large stock pot, pour enough cold water to cover it, and bring to a very low boil over medium-high heat. Skim the foam and never allow the water to come to a rapid boil to ensure a clear broth.

Add the vegetables, black peppercorns, bay leaves, and salt. Reduce to a very low heat, partially cover the pot, and simmer for about 45 minutes.

Pull out the chicken and place into a bowl to cool for a few minutes. Separate the meat from the bones and return the bones to the pot. Keep cooking the broth partially covered over low heat for 2 more hours, the strain the broth through a fine mesh sieve into a bowl. Once the broth is cool, cover the bowl with plastic wrap and refrigerate.

Make the dough: In a medium sized bowl, add the eggs, oil, water, and salt and mix with a wooden spoon until combined. Add the sifted flour in small quantities, mixing it thoroughly until a stiff dough is formed.

Cover a clean surface with a heavy dusting of flour and turn the dough onto it. Knead the dough until it is soft, supple, and no longer sticky, about 5-7 minutes. Place the dough into a bowl, cover with a kitchen towel, and let rest for about 30 minutes. 

Make the filling: Place 1 cup of dark chicken meat and ¼ cup of chicken skin into a food processor. Pulse a few times to combine, then add the sautéed onions, beaten egg, chopped parsley, salt, pepper, and a couple tablespoons of chicken stock and pulse a few more times until the mixture is combined but not mushy. Set aside. 

Shape the dumplings: Divide the dough into thirds, working with one piece at a time and keeping the remaining pieces covered. On a lightly floured surface, roll the dough into a rectangle. Roll the dough until it is so thin that it becomes see-through. Using a ruler and a pizza dough cutter, cut into 2½x2½-inch squares.

Place a heaping teaspoon of filling onto each square. Dip your finger into a cup of water, moisten two sides of the square, and pull one corner to meet the opposite one. Pinch the dough tightly and make sure there is no air space left. The dumpling should be in the shape of a triangle. Repeat with remaining dough and filling. Place the dumplings onto a prepared baking sheet sprinkled with flour. If you are not going to cook them right away, freeze them on the cookie sheet, and then transfer into a plastic freezer bag for storage. 

Reheat the broth over medium heat, and set aside.

Cook the kreplach: In a large pot, bring water to a boil with 2 teaspoons of salt. Drop the kreplach into the boiling water and cook for about 10 minutes The dough should be al dente, but cooked through. Take the dumplings out with a strainer, place into the bowls, and pour hot broth over them. 

Sprinkle with chopped parsley and serve. Kreplach can be stored in an airtight container in the refrigerator for 4 days.