Preheat oven to 350°.
Pulse pecan halves in a small food processor until it is a fine powder (but not butter). Stir in pumpkin pie spice, baking powder, xanthan gum, and salt.
In a medium bowl, combine butter, sugar, eggs, sweet potato and vanilla. Stir in pecan mixture.
Spray donut pan molds with cooking spray or grease generously with butter. Spoon batter into donut pan molds to fill, being careful not to overflow and cover center hole-maker.
Bake at 350° for 10-12 minutes, or until done. Let cool in pan for 4 minutes and turn out to a wire rack. Let cool.
Meanwhile, pulse brown sugar in a food processor until it is a fine powder. Add powdered sugar and water to make icing. Spoon evenly over donuts.