Prepare Rice Nog.
To make doughnuts:
In a bowl combine flour, baking powder, baking soda, salt and spices. Set aside.
Using an electric mixer on medium speed, beat margarine and granulated sugar until smooth. Add eggs or replacer one at a time and continue to beat until eggs are incorporated. Use a spatula to scrape down the sides of the bowl occasionally. Reduce the speed to low and gradually add rice nog. Mix until just combined. Add flour mixture and continue to mix until dough comes together.
Line 2 baking sheets with parchment paper and SPRINKLE GENEROUSLY (dough gets sticky otherwise) with flour (add a little on top of the dough too). Turn dough onto one of the baking sheets and top with flour. Flatten with hands until 1/2 inch thick. Use more flour if dough is still wet. Transfer to freezer until slightly hardened, about 20 minutes. Cut out doughnuts (or I like using a circle cutter for doughnut holes). Put cut outs on baking sheet. Refrigerate for 20-30 minutes.
Add enough shortening to deep sided pan for 3 inch deep. Line a plate with paper towels. When oil is 350 °F fry each doughnut for approx 60 seconds - golden brown - flip. Drain on towel.
Slowly whisk rice nog in with confectioner's sugar until it is a thick syrup. Dunk doughnuts in topping, sprinkle with nutmeg, and let rest.
Carefully check your spices for any cross contamination issues especially if you need to avoid nuts and/or sesame.
Gluten free all purpose flour can be used as needed. Add xanthan gum if your mix does not contain any.