Preheat the oven to 350 degrees F and spray a donut pan with non-stick spray.
In a large bowl, whisk together the flour, brown sugar, baking powder, pumpkin pie spice, and salt until well combined.
Pour in the melted vegan butter, pumpkin puree, oat milk, and vanilla extract into the dry mixture; stir well until everything is combined into a smooth batter.
Spoon the batter into each cavity of the donut pan, filling them to the top or use a piping bag for less mess.
Place the filled donut pan into your preheated oven and bake for 10-12 minutes or until the edges are slightly browned.
While your donuts cool slightly, whisk together all glaze ingredients in a medium bowl until a smooth glaze forms; adjust with oat milk as needed.