Preheat the oven to 350 degrees.
In a large mixing bowl, beat the melted butter, brown sugar, coconut sugar, vanilla, and apple cider. Then, beat in the eggs, cinnamon, nutmeg, baking powder, salt, corn starch, and gluten free flour blend. Scoop batter into a piping bag.
Grease a doughnut pan with melted butter or nonstick spray. Pipe batter into each doughnut well, until about 1/2 to 2/3 full. Bake for 9-12 minutes, until an inserted toothpick comes out clean. Allow to cool for a few minutes.
APPLE CIDER GLAZE: In a small bowl, melt the 2 Tbsp. of butter. Next, whisk in the apple cider. While doughnuts are still warm, dip one side of each doughnut into the apple cider glaze.
CINNAMON DRIZZLE: In a small bowl, whisk the powdered sugar, cinnamon, and apple cider. Then, whisk in the melted butter. Add more apple cider or powdered sugar, until a thick glaze is formed. Pipe or drizzle over the doughnuts.