Add chicken to the bottom of a large stock pot. Add in 2 cups baby carrots, 3 celery stalks, bay leaves, garlic, peppercorns, thyme, parsley, 2 onions (halved), water and salt. Bring to a boil and reduce to a simmer. Cover and simmer for 1½ hours. Take the chicken out, and pull all meat off the bones. Place the bones and skin back in to the pot and continue to simmer for another hour and half.
While the stock continues to simmer, make the noodles. Add egg, salt, chives, and milk to the bottom of a stand mixer fit with the dough hook. Mix the dough until combined, then turn the mixer up to a medium speed and knead the dough for 1-2 minutes.
Split the dough in to two balls. Add one ball to a heavily floured surface. Roll dough out until it's as thin as possible, and make sure to turn dough frequently and flour frequently so it doesn't stick. You want the dough to be about 1/16-inch thick. Use a sharp knife or pizza cutter to cut the dough into ¼-inch noodles. Once all of the noodles are cut, sprinkle with more flour and set aside. Repeat process with remaining ball of dough. Lay floured noodles out on a baking sheet while the stock finishes cooking.