For the poached chicken breasts: Place the chicken, leek, onion, celery, carrot, lemon, parsley, dill, thyme and bay leaf in a large pot and fill with water until the pot is 2-3 inches full from the top, about 3-4 quarts water. Cover and bring to a boil, then uncover and reduce the heat to simmer. Cook, uncovered, for 1 hour. Remove the chicken to large plate or bowl. Strain the cooking liquids and reserve for soup stock. Pull the skin and carcass away and chop the meat or shred it with forks.
To make the soup: Heat 2 tablespoons EVOO in soup pot or large Dutch oven over medium-high heat and add the leeks, onions, celery, parsnip or fennel, carrots, salt and pepper. Stir frequently for 10 minutes to soften the vegetables without browning them, then add the stock and one-third of the chicken meat to the pot. Cool and store the soup for a make-ahead meal and reheat over medium-high heat or, to serve immediately, reduce the heat to simmer and cook the egg noodles in another pot.
Boil water in a large pot, salt the boiling water and cook the pasta to al dente, with a good-bite left to it. Drain the pasta and toss with butter or a drizzle of oil; stir to combine and coat the noodles evenly.
Pour the soup over the noodles in soup bowls and top with fresh dill, parsley or reserved fennel fronds, if using.
Cook’s Note: Cook the egg noodles separately, even if you plan to serve soup right away. Add the noodles hot from cooking them to individual bowls and cover with the soup. Cook, cool and store, reheat the noodles in a microwave, covered, or combine with portions of the soup on the stovetop. If you combine the noodles with soup or cook them in soup they will bloat and the leftovers will not be as good as the original soup.