In saucepan, bring chicken stock to boil.
In essentials pan, saute onions, carrots and broccoli with butter. Add olive oil as needed if pan looks dry. Cook until onions are translucent and carrots are beginning to soften.
Add chopped chicken, bay leaves, oregano, basil, thyme, garlic, salt, pepper and hot chicken stock to skillet. Simmer 20-30 minutes until vegetables are softened. Adjust seasoning, as necessary.
Whisk cornstarch into half-and-half until smooth. Whisk into soup and simmer 5 minutes, until slightly thickened.
To make Dumplings: In medium bowl, mix flour, baking powder, salt and half-and-half. Swirl soup with wooden spoon and add heaping tablespoons into center of soup at strong simmer. Continue adding until all dumpling batter is used. Cover with lid and cook on high 2-3 minutes.
Serve topped with grated Parmesan and fresh cracked pepper.
