Preheat the oven to 350° F. Butter a 24-cup mini muffin pan or 12-cup regular pan.Bring the apple cider to a boil over high heat. Reduce the heat and simmer 10-15 minutes, until reduce to 1/2 cup. Remove from the heat and and stir in the melted butter. Let cool. In a large bowl, stir together the boiled cider, eggs, apple butter, maple, and vanilla until combined. Add the flour, whole wheat flour, baking powder, baking soda, cinnamon, cardamom, ginger, nutmeg, and salt. Mix until just combined. Divide the batter evenly among the prepared pan, filling 1/2-2/3 the way full. Bake 10-12 minutes for mini doughnuts or 18-20 for regular muffins, until just set. Remove and let cool 5 minutes, then run a knife around the edges to release.Meanwhile, melt 6 tablespoons butter in a skillet. Allow the butter to brown until it smells toasted, 3-4 minutes. Remove from the heat and mix in the vanilla.Combine the sugar and cinnamon in a bowl. Brush each doughnut with butter, then roll through the cinnamon sugar. Enjoy warm or at room temperature.