Melt butter in a large soup pot over medium heat. Stir in carrot, onion, celery, salt, and fresh thyme. Stir in chicken fat; cook and stir until the onions turn soft and translucent, 5 to 6 minutes.
Stir in roasted chicken broth and bring to a boil.
Season to taste with salt, if necessary; stir in egg noodles and cook until tender, about 5 minutes.
Stir in cooked chicken breast meat and simmer until heated through, about 5 minutes. Season with cayenne pepper, salt and black pepper to taste.
