Chicken and Dumplings

Name: Chicken and Dumplings
Ingredients: 1 lb. boneless skinless chicken thighs (5 to 6); 1 lb. boneless skinless chicken breast halves (about 3 pieces); 1/2 teaspoon fine sea salt plus more for cooking water; 1/8 teaspoon freshly ground pepper; 1 tablespoon unsalted butter; 1 large onion finely chopped; One 14 1/2-ounce can low-sodium chicken broth skimmed of fat; 1 1/2 teaspoons finely chopped fresh thyme; 2 tablespoons cornstarch; 2 tablespoons all-purpose flour; 2 cups low-fat (1 percent) milk; 3 carrots peeled and diagonally sliced 1/4 inch thick; 1/2 lb. green beans trimmed and cut in 1-inch pieces; 1/4 cup all-purpose flour; 1/2 cup yellow cornmeal; 2 teaspoons baking powder; 1/4 teaspoon fine sea salt; 2 tablespoons cold unsalted butter cut in bits; 2/3 cup low-fat (1 percent) milk