In medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon and nutmeg. Set aside.
In large bowl, beat eggs on medium speed until foamy, about 3 minutes. Gradually add brown sugar, crumbling with hands. Beat until smooth. Mix in cider and melted butter. Add flour mixture and stir with wooden spoon until combined.
On sheet of plastic wrap, with floured hands, pat dough into 1 3/4-inch thick disk (about 9-inch round); wrap with plastic. Refrigeraterate at lease 2 hours or overnight.
After dough has chilled, heat 8 cups of oil in a 3 1/2-quart heavy duty saucepan over medium -high heat until it registers 365 on deep fat frying thermometer.(Carfully heat oil to 365, using deep fat frying thermometer. Be sure that tip of thermometer is not resting on bottom of pot). While oil is heating, on lightly floured surface, roll out dough to 1/2-inch thickness. Cut into round donuts with donut cutter, or use 2 3/4-inch round cutter for the centers. You may also cut the dough into 3 1/12-inch x 1 1/2-inch strips. Set aside. Place confecners's sugar in medium bowl.
Using a slotted spoon carefully slip the donuts, sticks and donut holes, 3 or 4 at a time, into the hot oil. Fry until golden about 1 minute, turning once, about 2-3 minutes per batch. Drain donutson paper towel, then transfer still warm donuts to confectioners' sugar and roll to cover. Serve warm.