In a dutch oven over medium heat melt butter and heat olive oil. Add onion, celery, and carrots. Saute until they begin to soften; 3 to 4 minutes. Sprinkle in flour and stir constantly for about a minute, until no white flour can be seen.

Slowly whisk in chicken stock, stirring until the broth is smooth and there are no flour lumps. Bring to a boil and add shredded chicken. Reduce heat and simmer for 10 minutes or until the broth has begun to thicken and the vegetables are soft.

Meanwhile, make the dumplings. In a medium bowl, whisk together flour, baking powder, salt, pepper and a tablespoon of fresh chives if using. In a small bowl, whisk together buttermilk and egg. Add the buttermilk to the flour mixture, followed by the melted butter. Using a spoon or ice cream scoop, drop generous dollops of dumpling dough into the simmering pot, spacing them apart as much as possible.

Cover the pot and reduce heat to low. Cook, undisturbed, until the dumplings are puffed and completely cooked through, 18 to 22 minutes. You can test a dumpling by cutting it in half. There should be no raw bits of dough.

Remove the lid and portion among bowls. Sprinkle with fresh parsley and chives if using.