Cut the chicken into 4 pieces, cutting first in half along one side of the spine and then cutting off the thighs. Place the pieces in a large pot and cover with cold water. Turn the heat to high.
Add one carrot, one celery stalk, the onion, peppercorns, bay leaves, and garlic to the pot, along with one teaspoon of salt. Once the water boils, turn the heat to simmer and cover. Cook for 90 minutes.
Remove the pieces of chicken to a cutting board and allow to cool enough to handle. Strain the liquid from the pot into a large bowl using a cheesecloth or fine mesh strainer.
Place the strained stock back into the pot and add the remaining celery, carrot, and green onion. Add the remaining teaspoon of salt and bring to a boil. Turn the heat down to simmer for 12-15 minutes until the carrots are tender.
While the strained broth is simmering, remove the chicken skin and shred the meat. Return the shredded meat to the pot. Remove the pot from heat and add parsley. Cover and let rest for 5 minutes before serving.
Combine flour, dry milk powder, baking powder and salt; cut in shortening until crumbly. Add water gradually, mixing to form a firm ball. Divide dough; shape into 12 balls. Let stand, covered, for 10 minutes. Roll each ball into a 6-in. circle. With a sharp knife, cut a 1/2-in.-diameter hole in center of each.
In a large cast-iron skillet, heat oil over medium-high heat. Fry dough circles, one at a time, until puffed and golden, about 1 minute on each side. Drain on paper towels; if desired, serve warm with butter, honey and fresh lemon juice.