The best baked pumpkin donuts with a rich and nutty brown butter glaze. These will disappear in no time.
Melt the butter in a small saucepan over medium heat and heat until golden brown specks appear in the bottom of the pan, swirling the pan occasionally. The butter will get foamy and if you swirl the pan around, you will see brown bits at the bottom and it will have a nutty smell. Remove from heat and pour into a medium bowl, using a rubber scraper to get all the brown bits at the bottom. Add the powdered sugar and vanilla and stir until smooth and well combined. Add enough milk, as needed, to reach desired glaze consistency. Dip tops of cooled donuts in glaze and set on a wire rack and allow glaze to harden.