To prepare the dumplings, in a bowl, combine the flour, cheese, baking powder, and 3/4 teaspoon of salt. In a small saucepan, bring the milk and butter to a simmer over low heat; season with black pepper. (Or zap the milk and butter in a glass measuring cup in the microwave until the butter is melted.) Add the milk mixture to the dry ingredients and using a rubber spatula, stir to combine. Heads up -- the mixture will be pretty dry. Set aside.

In a second large saucepan, heat the oil over medium heat. Add the onion, carrots, and celery. Cook until the onions are translucent, 3 to 5 minutes. Add the garlic and cook until fragrant, 45 to 60 seconds. Add the stock and bring to a boil over high heat. Decrease the heat to low. Using a small ice cream scoop or tablespoon, drop the dough, about 1 tablespoon at a time, into the simmering stock. Cover and simmer until the dumplings are cooked through and the vegetables are tender, about 20 minutes.

To assemble, add the chicken and cook just until heated through, about 5 minutes. Add the parsley. Taste and adjust for seasoning with salt and pepper. Serve immediately.