Chicken Noodle Soup

1 (3 1/2) pound chicken, giblets removed
1 onion, peeled and quartered
1 rib celery, cut in chunks
2 teaspoons kosher salt
3 cloves garlic, lightly smashed
1 tablespoon ketchup
2 quarts cold water, or more as needed
1 tbsp butter
1/2 cup diced carrots
1/2 cup diced onions
1/2 cup diced celery
1/4 tsp fresh Thyme
2 tbsp melted chicken fat
2 quarts roasted chicken broth
4 ounces uncooked wide egg noodles
Chicken breast halves from roasted chicken
Pinch of Cayenne pepper
Pinch of Salt

To make the roasted chicken broth:

Preheat the oven to 400 degrees F. Place chicken, onion, and celery in a Dutch oven. Sprinkle salt over the top of the chicken. Roast chicken, uncovered, in the preheated oven until chicken is no longer pink inside, the skin is browned, and an instant-read thermometer inserted into the thickest part of a thigh reads 160 degrees F, 45 minutes to 1 hour. Transfer chicken to a plate until cool enough to handle. Once cool, pick the meat from the bones; set aside chicken breast meat for use in soup. 

Remove chicken fat from Dutch oven, leaving the brown flavor bits in the bottom of the Dutch oven. Place the Dutch oven over medium-high heat. Return chicken bones and dark meat from drumsticks and thighs to the pot. Add garlic cloves, ketchup and cold water. Bring to a boil, and use a spoon to scrape up and dissolve the brown flavor bits from the bottom of the Dutch oven. Reduce heat to low and simmer for 3 hours, adding more water if needed to retain same level. As broth simmers, occasionally skim off and discard any foam that rises to the surface. Remove and discard bones, meat and vegetables. Strain broth through a fine mesh sieve; set aside for soup.

Directions for soup:

Melt butter in a large soup pot over medium heat.  Stir in carrots, onions, celery, salt and fresh Thyme.  Stir in chicken fat. Cook and stir until 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.  Season with Cayenne pepper, salt to taste.