In a large mixing bowl beat together sugar and butter until mixture is pale and fluffy, 4-6 minutes. Add eggs, one at a time, beating one minute after each.
In a medium sized bowl whisk together the flour, salt, baking powder, baking soda, cinnamon, and nutmeg. Set aside.
Pour buttermilk, boiled cider, and vanilla into sugar/butter/egg mixture. Mix well, and don't worry if the mixture looks a bit curdled; it'll smooth itself out. Add flour mixture and combine gently just until fully moistened.
Line two baking sheets with waxed paper or parchment paper and dust generously with flour (very important to make sure the doughnuts don't stick). Turn dough out onto one baking sheet and pat gently into 3/4" thickness. Sprinkle dough with additional flour, cover with plastic wrap and freeze for 10 minutes to firm up. Remove dough from the freezer; use a lightly floured 3" doughnut cutter to cut out about 18 doughnuts. (You may gather the scraps and roll again as needed, but you may need to chill the dough more to firm it up.) Place cut doughnuts on the other baking sheet as you go; then transfer to the freezer for 5 minutes to firm up again.
Line a plate with a few paper towels and set it nearby. In a Dutch oven or a large pot, heat 3" of oil to 370 degrees (test with an instant-read thermometer). Drop 3 or 4 doughnuts into the oil, being careful not to crowd the pan. Cook 1 minute then flip and cook 1 minute on the other side. Repeat with the remaining dough (if you find that the dough is getting too soft, refreeze for a few minutes). Remove from oil and place on paper towels. Let doughnuts cool for about 3 minutes. Roll them in the cinnamon sugar mixture or sprinkle with confectioners' sugar. Serve immediately.
* You can make your own boiled cider by slowly boiling 1 cup cider under low heat for approx. 30 minutes until it is reduced to 1/3 cup.