Preheat waffle iron according to manufacturer's instructions.
Combine almond flour, arrowroot starch, sugar, baking powder, xanthan gum, and salt in a medium bowl. Combine milk, egg, vanilla paste, and butter in a measuring cup or medium bowl. Add milk mixture to flour mixture; stir until just combined.
Spoon about 2 tablespoons mixture into the center of hot waffle iron; cook according to manufacturer's instructions. Cool slightly on a wire rack. Repeat with remaining batter.
Combine icing ingredients with a wire whisk to make a thick glaze. Add more sugar or milk to achieve desired consistency. Dunk tops of waffle donuts into glaze. Allow excess to drip off, sprinkle with extra sprinkles, and return to wire rack for glaze to set.