Preheat the oven to 350 degrees Fahrenheit and prepare a donut pan by greasing with butter or nonstick spray. Set aside.
In a small sauce pot, make an apple cider reduction by simmering the apple cider over medium high heat until it is reduced to about ½ cup. This will take about 10 minutes of active simmering. Remove from heat and cool until it returns to room temperature.
In a large bowl, whisk together the dry ingredients, flour, baking powder, ground cinnamon, light brown sugar and white sugar until well incorporated.
In a separate bowl, combine wet ingredients, egg, vanilla milk and cooled cider reduction.
Slowly mix flour mixture into wet ingredients. Stir just until combined. Batter will be thick.
Scoop or pipe the donut batter into the prepared baking pan, filling each mold halfway full. Gently pat the sides of the donut tray to help the batter level out.
Bake for 10 minutes or until a toothpick inserted in the center comes out clean. Turn out the doughnuts onto a wire rack or parchment paper to cool.
While the doughnuts are cooling, prepare the cinnamon sugar coating by mixing the white sugar with cinnamon.
Dip each cooled doughnut in the melted butter and then into the cinnamon sugar mixture.