Step 1: Reduce the apple cider. Pour 1.5 cups of apple cider into a small saucepan and simmer over medium heat until reduced to approximately rac{3}{4} cup (about 10-15 minutes). Set aside to cool slightly.
Step 2: Preheat your oven to 350°F (175°C). Lightly grease a standard 6-cavity donut pan. If using a 12-cavity pan, repeat greasing for the second batch.
Step 3: In a medium bowl, whisk together the gluten-free flour blend, baking powder, baking soda, 1 teaspoon ground cinnamon, nutmeg, allspice, and salt.
Step 4: In a separate large bowl, combine the cooled reduced apple cider, rac{1}{2} cup granulated sugar, light brown sugar, eggs, rac{1}{4} cup melted butter, milk, and vanilla extract. Whisk until well combined.
Step 5: Add the dry ingredients to the wet ingredients. Mix with a spatula or whisk until just combined. Do not overmix; a few small lumps are okay.
Step 6: Spoon the batter into the prepared donut pan cavities, filling each about two-thirds to three-quarters full. Alternatively, transfer batter to a piping bag with a wide tip or a Ziploc bag with a corner snipped off for easier filling.
Step 7: Bake for 12-15 minutes, or until the donuts are golden brown and a toothpick inserted into one comes out clean.
Step 8: While the donuts are baking, prepare the cinnamon-sugar coating. In a shallow dish, combine the rac{1}{2} cup granulated sugar and 2 teaspoons ground cinnamon. In a separate small bowl, melt the remaining 4 tablespoons of butter.
Step 9: Immediately remove warm donuts from the pan and transfer to a wire rack. While still warm, brush each donut generously with melted butter, then roll thoroughly in the cinnamon-sugar mixture to coat completely. Repeat with the remaining donuts.
Step 10: Let the coated donuts cool slightly on the wire rack before serving. Enjoy them warm for the best flavor and texture.