Preheat oven to 350
Using a hand mixer, cream together butter and sugar
Add the eggs and vanilla and mix well
In a separate bowl combine flour, baking powder, salt, nutmeg and cinnamon
Add dry ingredients to the wet ingredients and slightly mix together, add milk and mix thoroughly
Fill the wells of a non stick donut pan with batter (you may find it helpful to place batter in a pastry bag and squeeze into wells) and bake 15-20 minutes
If making donut holes, fill the wells of non stick donut hole pan and bake 7-9 minutes
Turn out donut/donut holes to cooling rack
Allow donuts to cool before icing
Coat donut holes while still warm