Simmer 1.5 cups of apple cider in a small saucepan over medium heat until reduced to 1/2 cup (approximately 15-20 minutes); allow to cool to room temperature before use.
Preheat oven to 350°F (175°C) and apply non-stick cooking spray to two 6-cavity donut pans.
In a large mixing bowl, whisk together the gluten-free flour, granulated sugar, baking powder, baking soda, 1.5 teaspoons cinnamon, nutmeg, cardamom, and salt.
In a secondary bowl, whisk the cooled apple cider reduction, egg, 2 tablespoons melted butter, vanilla extract, and milk until the emulsion is uniform.
Incorporate the liquid mixture into the dry ingredients and stir until just combined; avoid over-mixing to prevent a gummy texture.
Transfer the batter to a piping bag fitted with a large round tip or a zip-top bag with the corner excised.
Pipe the batter evenly into the donut pans, filling each cavity approximately 2/3 full.
Bake for 10-12 minutes or until the internal structure is set and a digital probe or toothpick returns clean.
Cool the donuts in the pan for 5 minutes, then invert onto a wire rack.
Prepare the coating by mixing the 1/2 cup sugar and 1 tablespoon cinnamon; while donuts are warm, brush surfaces with 4 tablespoons melted butter and roll in the sugar mixture until fully encapsulated.