Add the chicken to the water in a stockpot and bring to a boil; simmer, covered, about 20 minutes or until tender. Remove the chicken to a plate to cool. Add the onion, garlic, celery, and carrots to the stock and bring to a simmer. Cut or tear the chicken into 5 cm pieces and return it to the stock. Simmer for about 30 minutes, or until all the vegetables are very tender. Stir the cornstarch mixture into the stock if you like a thick sauce. DUMPLINGS: While the vegetables are cooking, bring to a boil 1- quarter cups water in a small pan. Turn off the heat and add three sprigs of rosemary. Cover and let steep for 30 minutes. Strain the rosemary tea and mix with about 2 cups of biscuit mix, slightly more if mixture is very gooey. Bring the chicken stock back to a low boil and drop scant teaspoons of dumpling batter into the bubbles. Gently push each dumpling aside with a spoon to keep dumplings from clumping together. Add two more rosemary sprigs, lower heat, cover, and simmer 5 to 10 minutes.