Preheat the oven to 350°F (175°C). Grease a donut pan.
In a large bowl, whisk together the gluten-free flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and sea salt. Set aside.
In a medium bowl, combine the pumpkin puree, avocado oil, brown sugar, eggs, sugar, almond milk, and vanilla extract. Whisk until smooth.
Slowly add the wet ingredients to the dry ingredients, mixing until well incorporated.
Transfer the batter into a large zip-top bag, cutting a small hole in one corner. Pipe the batter into the prepared donut pan, filling each mold about 3/4 full.
Bake for 11-12 minutes or until the tops are golden and bounce back when touched. Let cool in the pan for 2 minutes before transferring to a wire rack.
For the icing, combine brown sugar, almond milk, and dairy-free butter in a small saucepan over medium heat. Stir until smooth and let simmer for 1 minute.
Remove from heat, whisk in vanilla extract and powdered sugar, and let cool for 5 minutes.
Dip the cooled donuts into the icing, allowing excess to drip off. Let the icing set on the donuts by placing them back on the wire rack.