The sweetness of the potatoes balances the savory filling of the pot pie. Slideshow: More Chicken Recipes
Preheat the oven to 425°F. Pierce the sweet potatoes all over with a fork then drizzle with the oil and wrap in aluminum foil. Bake the sweet potatoes until tender, about 1 hour. Let cool to warm and peel, then slice into 1/2-inch thick rounds and reserve.
In a large cast-iron or heavy skillet, heat the oil over medium high heat until hot, then stir in the onion, garlic, carrots, potato, 3/4 teaspoon salt and 1/2 tea-spoon pepper. Cook, stirring occasionally, until golden, 8 to 10 minutes. Stir in the flour and cook, until incorporated, about 2 minutes. Pour in the stock and bring to a boil, then stir in the chicken. Season the filling with salt and pepper to taste.
Transfer the filling to a 3-quart baking dish. Place the sweet potato rounds over the filling, the sprinkle with a large pinch each of salt and pepper and drizzle with the melted butter. Bake the pot pie until the filling is bubbling, about 15 minutes.