Make the homemade noodles. In a mixing bowl, combine flour, salt, egg, and milk. Mix until you produce a slightly sticky ball of dough. Flour the counter and roll out the dough to ⅛-inch thickness. Side Note: You want them very thin because they thicken when they cook.
Cut noodles (I use a pizza cutter) to the desired size and place them on parchment paper.
Set aside and let the noodles dry out on the counter for at least 1 hour before adding them to the soup.
Meanwhile, prepare the soup by sautéing the onions in butter or olive oil in a large Dutch oven, stirring often, until soft, about 5 minutes.
Add carrots, celery, garlic, and thyme (or basil) and cook, stirring constantly, for 1 minute.
Add broth, bouillon, bay leaf, and chicken, then season with sea salt and freshly cracked pepper to taste.
Bring to a boil, then reduce the heat and simmer for 45-60 minutes, or until veggies are tender.
Add the noodles to the soup and cook until tender.
Add fresh parsley, then taste and re-season if needed.