In a small saucepan, bring cider to a rapid boil and cook over high heat until reduced by half, about 12 minutes. Cool completely.
Whisk together flour, brown sugar, baking powder, salt, baking soda and spices. In a separate bowl, whisk eggs, melted butter, buttermilk, and cooled cider; stir into dry ingredients just until moistened (dough will be sticky). Refrigerate, covered, 1 hour (up to 24 hours) or until firm enough to shape.
Divide dough in half. On a floured surface, pat each portion to 1/2-inch thickness; sprinkle with flour as needed to reduce stickiness. Cut with a floured 3 inch biscuit cutter. Make hole in the center of each 3 inch circle with a 1 inch biscuit cutter.
In an electric skillet or deep fryer, heat oil to 325°. Use a thermometer to keep an eye on the oil temperature throughout the frying process. Fry doughnuts, a few at a time, until golden brown, 2-3 minutes on each side. Fry doughnut holes, a few at a time, until golden brown and cooked through, about 1 minute on each side. Drain on paper towels; cool slightly. If desired, toss donuts in spiced sugar after draining but while donuts are still hot.
Spiced Sugar: In a shallow bowl, mix 3/4 cup sugar and 2-3 tablespoons ground pumpkin pie spice. Toss with warm doughnuts. Yield: 3/4 cup.