Place the chicken in a pot and cover with water. Cover and cook over medium heat for 1 hour. Remove chicken from pot, save the water, and let cool. Shred the chicken and place in the bottom of an 11x7 baking dish. Spread the veggies over the top of the chicken.
Whisk together the flour, milk and butter, pour over the chicken. Whisk together the broth, soup, salt and pepper, pour over the casserole, DO NOT STIR. Bake at 350 degrees for 45-50 minutes. Let sit for a few minutes before serving.