Making the broth: Put the chicken pieces and parsley in a large stockpot. Add water to cover. Bring to a boil. Once it starts to boil, turn the heat down to medium-low and simmer for 2 hours. Line a strainer with cheesecloth and strain. Put the broth in a clean pot on low heat. Skim off the top. Season with sea salt and pepper. Pick out the good chicken meat from the cheesecloth and set aside.
Making the pasta: Into a food processor, add the unbleached flour and eggs. Pulse until crumbly. Take the dough out and place on a floured surface. Knead the dough until silky, about 5 minutes. Wrap in plastic wrap and let rest for 30 minutes. Roll out the dough by hand, or using a pasta machine, until about 1/8-inch thick. Slice into lengths the size of the baking dish. Preheat the oven to 400 degrees F.
Making the lasagna: Place a layer of pasta, then some mozzarella, Parmigianno, chicken meat and a ladle of broth. Repeat three times. Finish with a top layer of cheese and bake until the cheese is melted and golden brown on top, about 30 minutes. Plate the lasagna in a shallow bowl, add a ladleful of broth and enjoy.