Make dumpling dough. In a large bowl, mix together flour, baking powder, salt, and black pepper. Make a well in the center and add buttermilk and melted butter. Mix all ingredients together until a dough ball forms. Do not over mix. Set dough ball aside.
In a large pot over low to medium-low heat, add 4 tablespoons butter and the diced onion. Cook onions down until very soft, about 5-6 minutes.
When onions are tender, add carrot, celery, garlic, rosemary, and thyme to the pot. Cook on low to medium-low about 5-7 minutes, stirring occasionally.
Add flour to the pot with the vegetables and cook about 2-3 minutes, stirring frequently.
Add turkey stock, half and half, cream of chicken soup, and diced turkey to the pot. Stir all ingredients together and cook on low while you make the dumplings.
Roll and cut the dumplings. Add a light dusting of flour to your countertop and a rolling pin. Turn the dumpling dough out onto the counter, and knead a few times. Then roll out into a rectangular shape about ¼" thick. Use a pizza cutter or knife to cut into 1" squares.
Mix about half of the dumplings in to the turkey soup mixture. Then lightly place the remaining dumplings on top of the soup. Cover and simmer about 20 minutes, stirring occasionally. After 20 minutes, add salt and pepper to taste.
Serve hot and enjoy!