To prepare the dumplings, in a bowl, combine the flour, baking powder, parsley 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. Add the milk mixture to the dry ingredients and stir to combine.
In a second large saucepan, heat the oil over medium heat. Add the carrots, onions and sweet potatoes. 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. Reduce the heat to simmer. Add the chicken and thyme.
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 and chicken are cooked through and the vegetables are tender, about 20 minutes. (The best way to see if the dumplings are cooked is to remove one from the pot and let it cool slightly. Using a chef's knife, halve the dumpling. If the center looks dry, it is cooked. If the dumpling looks gummy or wet, let them cook a bit longer.)
Stir in the spinach; cover and continue cooking for an additional 30 to 45 seconds. Taste and adjust for seasoning with salt and pepper.