Cook over medium heat, stirring constantly, until thickened and bubbly. In a stockpot, bring the chicken, water, onion, celery, carrot and 1/2 teaspoon salt to a boil. Stir in salt and pepper. Reduce heat; cover and simmer for 50-60 minutes or until chicken is tender. In a large saucepan over medium high heat, combine the chicken meat, chicken broth, salt and pepper. Bring to a boil and reduce heat to low. Directions. Set aside until cool enough to handle. Top with pastry pie crusts. Combine broth and half and half, also add ½ cup water; gradually stir into vegetable mixture. Pour chicken mixture into a greased shallow 2 quart casserole. Step 1. … Add chopped chicken, stirring well. Cover and let simmer for 30 minutes, or until chicken is no longer pink in the center and the juices run clear. Remove chicken and vegetables from broth.