Step 1 Place the chicken breasts and thighs, onion and carrot in a saucepan. Add water to cover and 1 teaspoon of salt. Add the peppercorns. Bring to a boil. Reduce the heat and simmer until the chicken is tender, about 25 to 30 minutes. Remove the chicken from the broth. Strain the broth with a fine mesh strainer. Add water to measure 5 cups. Set aside. Cut the chicken into bite-size chunks. Set aside.
Step 2 Melt the butter in a 4-quart saucepan. Cook the diced onion, celery and carrots over medium heat until tender, 5 minutes. Stir in the flour and cook 2 minutes. Add the reserved broth and potatoes. Cover and simmer until the potatoes are tender, about 10 minutes. Stir in the chicken bouillon and rosemary. Season to taste with salt and pepper. Heat to boiling, stirring until thickened, about 2 minutes. Mix in the chicken. Turn into a 13-by-9-inch baking pan. Keep warm while preparing the biscuit dough.