Place the chicken carcass, the giblets, and the neck into a large stockpot along with several celery ribs, 2-3 carrots, 1 onion, peeled and cut in half, a few peppercorns, a few pieces of whole cloves and a bay leaf. Add water until the chicken is just covered. Cover and bring to a simmer. I like to cook my stock for about 24 hours to allow the bones to break down. Strain the stock and discard all of the bones and vegetable pieces.

Melt one tablespoon of butter in a large soup pot. Add the mushrooms and cook until they are soft and cooked through. Add the garlic and the oregano and cook just a moment longer.

Add the remaining butter and the flour and stir to make a roux. This will help make your soup thick and creamy. Slowly add the stock one cup at a time. Stir and allow the soup to thicken slightly before adding more liquid. Begin by adding three cups of stock. Save the remainder of stock until the end and only use if your soup is too thick.

Next add the milk, rice and chicken. Bring the soup to a slow simmer and cook for 20-30 minutes longer. If necessary, add additional stock to thin the soup to your desired consistency. Any unused stock can be frozen for later use.