Preheat the oven to 400°F. Make the doughnuts: Place the two sweet potato halves on a baking sheet, cut sides down. Bake until soft, about 35 minutes. When cool enough to handle, scoop out the flesh, discard the skins, and mash the flesh. Measure 1/2 cup sweet potato mash and set aside (save any remaining mash for another use).
Meanwhile, into a cast-iron pan, pour vegetable oil about 3 inches deep. Heat the oil to 350°F on a candy thermometer.
Make the glaze: In a bowl, add the powdered sugar, whisking in the maple syrup, 1 tablespoon at a time to taste, until the glaze is thick but pourable.