Add butter and flour to a large saucepan under medium heat. Stir until the butter melts, then WHISK the flour and butter together, cook about one more minute while you whisk. Add the diced green peppers, onion,celery, and carrot. Saute the vegetables about 5 minutes until softened.. Add 1 cup of milk, 6 cups of chicken broth and 1 cup cream to the saucepan. Add the rice to the pan. Bring to a boil , reduce heat and simmer until rice is tender. Add the cooked chicken and salt and pepper to taste. Serve immediately.
