Chicken and Rice Soup

1 small onion, chopped
1 carrot, shredded
About 4 tbsp butter
1/3-1/2 cup flour
4 cups chicken stock
2 cups milk
1 tsp salt
1/4 tsp pepper
parsley
1 cup white or wild rice
chicken - cooked and chopped

Saute onion and carrot in butter until tender and the onions are clear.  Stir in flour and seasonings to thicken.  Slowly stir in broth, keeping mixture smooth.  Stir in milk, chicken, and rice.  Bring to a boil.  Cover; reduce heat and simmer until rice is cooked (20-30 minutes) and soup is thickened a bit.