Creamy Chicken Noodle Soup

I may have mentioned once or twice here how much I love soup.  I often order cream of chicken soup when out at a restaurant and I can tell immediately how much sodium is in those soups.  I found this recipe and liked that it wasn't too rich and could easily be tweaked.  I look forward to making this one my own.

1/2 whole chicken, cut up (I may see if Chris will smoke a chicken for me)
2 tbsp. butter
2 ribs celery
1/2 onion, chopped
2 tbsp. all purpose flour
1 tsp. salt
1/4 tsp. freshly cracked black pepper
1 1/2 C. thin egg noodles
1/2 C. half and half

Rinse chicken and pat dry.  In a Dutch oven or large saucepan, cover chicken with water and bring to a boil.  If you're starting with a smoked chicken, skip these steps.  Reduce heat and simmer 40 minutes or until chicken is tender and cooked through.  Remove chicken, reserving the broth.  Shred chicken and remove bones.

Heat Dutch oven or large saucepan over medium heat.  Add butter, celery and onion; cook until softened.  Stir in the flour and cook until golden brown.  Whisk in reserved broth, salt and pepper.  Bring to a boil; stir in noodles and cook until tender, stirring occasionally.  Stir in reserved chicken and half and half.