Preheat your oven to 375°F. Lightly grease 2, 6-cavity donut pans.
In a large mixing bowl, mix together the wet ingredients: eggs, sugar, brown sugar, oil, pumpkin puree and vanilla. Stir until combined.
In a separate bowl, whisk together the dry ingredients: gluten-free flour, pumpkin spice. Gradually add the dry ingredients to the wet ingredients, mixing until a smooth cake batter forms. I used a whisk but you can also use a hand mixer or stand mixer.
Pour the donut batter into the prepared muffin tins.
Bake in the preheated oven for approximately 20-25 minutes, or until a toothpick inserted into the center of the donut comes out clean.
While the donuts are cooling on a wire rack, prepare brown sugar glaze. In a mixing bowl, beat dairy-free butter, brown sugar, dairy-free milk, vanilla and until smooth and creamy. Slowly add the sifted powdered sugar and finally the vanilla extract.
For best results, wait until the donuts have cooled completely. Remove from donut molds and drizzle the glaze on top.
Optional: Sprinkle with chopped pecans.