I've been making a left-overs chicken soup for years now, using the carcas of the Sunday roasted chicken and chucking in any left over meat. Domini Kemp in her new book "Domini at Home: How I Like to Cook" has included a recipe using the full chicken in The Metro newspaper today.
N.B. Don't bother peeling veg/removing onion and garlic skin cos it's all tossed away after anyway.
1 chicken, minus giblets
a piece of ginger, thick sliced
1 onion, halved
3 carrots, halved lengthways
1 whole garlic, halved
few sprigs thyme
a bay leaf
3 tsp turmeric
S & P
few splashes Worcestershire sauce ("wooster-sheer" not "wor-sester-shyre" as my daughter calls it!)
Using saucepan big enough to hold the chicken, half fill it with water and pop in the chicken and all the veg. Slowly bring to boil then turn up heat to let it boil rapidly for 2 mins. Turn down to low, use a spoon to skim away frothy scum from surface. Keep on lowest setting, partly cover and simmer for 2 1/2 hours.
After this time carefully remove the chicken to a bowl, and continue to simmer the soup gently to reduce a little. If you raise the heat it will go cloudy. Taste for flavour/seasoning and if happy drain into another pot through a colander, chucking out veg (or save for your dog for dinner). If the chicken is cool enough to handle, strip it of all meat, chucking away skin & bones, put meat in with stock and serve. I love to drop a couple of boiled potatoes into the soup bowl along with this which is waht my mum always did with the left-overs turkey soup at Christmas.