In a medium stockpot or Dutch oven over medium-high, heat the oil. Add the next seven ingredients and cook for 5 minutes. Add the broth, stir, and bring to a simmer.
Meanwhile, in a medium bowl, stir together the flour, baking powder, milk, and 1/2 teaspoon of the salt until a stiff batter forms.
Add the turkey and remaining salt to the stockpot and stir. Drop the batter by the spoonful onto the surface of the stew. Cover the pot and simmer until the dumplings are cooked through, about 15 minutes.
White whole wheat flour is a great option for picky eaters. It has the nutritional advantages of whole wheat but the lightness and taste of all-purpose flour (which can be substituted here).