In the dutch oven, melt the butter over medium heat. Add the onions, carrots, and celery. Cook until onions are translucent. Add garlic and cook for 1 additional minute.
Add the broth, a bay leaf, rosemary, sea salt, and black pepper.
Shred or chop the cooked chicken and add it to the pot.
Simmer for 30 minutes.
Add the egg noodles into soup and simmer for 12 minutes, stirring occasionally.