1. Beats eggs, sugar and butter until light and fluffy.
2. In a separate bowl, sift together flour, baking powder, baking soda, salt and nutmeg.
3. Gradually add buttermilk to egg mixture, stirring until well blended.
4. Slowly add flour mixture, beating only until combined. Add orange rind.
5. Cover bowl. Chill for 1 hour.
6. On well-floured surface, roll dough out to ½ inch thickness.
7. Let rest 10 minutes.
8. Cut doughnuts with a glass or doughnut cutter. Cut close together.
9. Repeat steps 6 to 8 with remaining dough and trimmings.
10. Heat oil in saucepan or frying pan until 375F. Gently drop a few doughnuts at a time in hot oil.
11. As doughnuts rise, turn them over with a slotted spoon.
12. Fry until golden brown and cooked through.
13. Remove and drain on double paper toweling.