Preheat oven to 350 °F. Brush two 6-cavity donut baking pans with melted butter or spray with cooking spray. If making donut holes, use two 24-cup mini muffin pans.
Heat the apple cider in a saucepan. Simmer over medium heat until it has reduced to ½ cup, stirring occasionally. This will take about 20 minutes. Remove from heat and let the reduced cider cool. This step can be done ahead of time and the cider can be refrigerated.
Whisk the flour, baking powder, baking soda, cinnamon, nutmeg, cardamom and salt together in a large bowl.
Whisk the reduced apple cider, buttermilk, sugar, egg, vanilla and melted butter together in a large bowl.
Add the dry ingredients to the wet ingredients and stir until just combined (the batter will have some small lumps). Do not overmix.
Spoon or pipe the batter into the prepared donut pans, filling the wells about ¾ full. You can make a piping bag by taking a large zipped-top bag and cutting one of the corners off. If making donut holes, spoon or pipe the batter into a mini muffin pan, filling the wells about ½ full.
Bake donuts in the oven for 10-12 minutes until puffed up and lightly browned. Bake donut holes for 9-10 minutes. Remove from oven and cool for a few minutes. Transfer donuts to a wire rack.
To make the cinnamon sugar topping, mix the sugar and cinnamon together in a shallow bowl. Brush the tops of the donuts with a little melted butter and then dip them in the cinnamon sugar, coating them well.
The donuts are best when served immediately. They can be stored in an airtight container at room temperature for up to 2 days or in the refrigerator for up to 5 days. They can also be frozen for up to 3 months.