Preheat the oven to 350º and spray two nonstick 6-cavity doughnut pans with cooking oil. In a large bowl, whisk the flour with the sugar, baking powder, nutmeg and 1/2 teaspoon salt.
In a medium bowl, whisk the eggs with the oil and milk until smooth; add to the flour mixture and whisk until combined.
Spoon the batter into 10 cavities of the prepared doughnut pans until about three-quarters full. Bake for 18 to 20 minutes, until a toothpick inserted in the center of a doughnut comes out clean. Let the doughnuts cool slightly, then fill a pie plate with confectioners’ sugar and dredge the doughnuts in the sugar to coat completely.