In a medium saucepan bring apple cider to boil over medium heat. Stir in finely chopped apple. Lower the heat and simmer uncovered for about 25 minutes or until reduced to 1 cup. Set aside to cool.

Meanwhile, in a medium bowl, whisk together the flour, baking powder, 1 teaspoon cinnamon, baking soda, salt and nutmeg. Set aside.

In a large bowl, beat 1 ½ cup sugar and butter with an electric mixer on medium speed for 2 minutes. Add eggs, beating just until combined. Beat in the cooled, reduced apple cider and buttermilk. Add flour mixture; beat until just combined and the dough starts to form. The dough will be very sticky. Do not add additional flour. Set aside.

Meanwhile combine the remaining ½ cup sugar and the remaining 1 tablespoon cinnamon in a shallow dish for coating. Set aside

When the oil reaches temperature, scoop about 1 ½ tablespoons of dough with an ice cream scoop or spoon and gently drop it into the hot oil. Repeat to place 4 to 5 doughnut holes into the hot oil at a time. Do not overcrowd the pot. Cook for 1-2 minutes turning multiple times, or until golden brown in color. Remove with slotted spoon and drain the cooked doughnuts on a paper towel-lined baking sheet.

While the doughnut holes are still warm, roll in a cinnamon sugar mixture to coat. Serve warm.