Preheat oven to 400℉.
In a large bowl, mix unsalted butter and granulated sugar until thoroughly combined. Then add egg, canned pumpkin, vanilla extract and milk. Mix well.
Into the same bowl, add all of the dry ingredients: gluten free flour, baking powder, xanthan gum, cinnamon, nutmeg, ginger and salt. Mix until fully incorporated and no lumps remain.
Grease two 6-well donut pans using a bit of melted butter (if not using nonstick). Using a piping bag or a plastic sandwich bag with the corner cut off, pipe the dough into each well of the pans. Ensure the dough is even and fills ¾ of each well.
Bake donuts for 10 minutes. They are done when an inserted toothpick comes out clean. Cool donuts on a wire rack.
Once donuts are cool and ready to be iced, make the maple brown sugar glaze by mixing melted unsalted butter, brown sugar, maple syrup, icing sugar and pinch of salt in a small bowl. Glaze should be smooth and free of any lumps.
Add glaze into a clean piping bag (or sandwich bag with the corner cut off) and pipe across the tops of each donut. A small hole in the piping bag will result in a thinner icing strip.
Enjoy immediately, or allow donuts to sit for a few minutes for icing to set.