In a large mixing bowl, beat packed brown sugar, eggs, salt and spices. Beat until thick, about 3 to 5 minutes. Gradually beat in the cooled melted butter, then beat in the apple cider.
Combine flours, baking powder and baking soda. Add to batter, beat just until blended. Cover and refrigerate 1 hour. Divide dough in half.
Turn dough onto a lightly floured surface, pat into 1/2 inch thickness, cut with a floured 2-1/2 inch doughnut cutter, repeat with remaining dough.
In an electric skillet or deep-fat fryer, heat oil to 375 degrees.
Fry doughnuts, 2 or 3 at a time, for 2 minutes per side or until golden brown. Drain on paper towels
Sprinkle with powdered sugar or cinnamon-sugar.