Prepare the vanilla pudding according to directions on the box. Place in refrigerator to set and chill.
To make the dough: In a small bowl combine yeast and warm water. Sprinkle sugar on top and mix lightly. Allow to sit until foamy, around 10 minutes.
When yeast mixture is ready, in a large bowl combine it with flour, cinnamon, nutmeg, salt, eggs and butter, using a wooden spoon until a sticky dough forms.
On a floured surface, knead dough until it is smooth, shiny and bounces back when touched, around 8 to 10 minutes. Place in an oiled bowl and allow to rise 1 1/2 to 2 hours, or until doubled in size.
To assemble: On a lightly floured work surface, roll dough to 1/4-inch thickness. Using a 2 1/2-inch round cutter or glass, cut rounds. You may have to roll out the dough a few times. Cover with plastic wrap and let rise another 20 to 25 minutes.
Heat oil in a pot on medium heat until a thermometer measures 370 degrees. If you don’t have a thermometer, raise the heat to low-medium heat and test one of the doughnuts. If the oil immediately starts bubbling and the donut begins browning, it is the right temperature. If it doesn’t bubble at all, heat needs to be higher. If the oil splatters or the doughnut starts browning too quickly, heat needs to be turned down.
Using a slotted spoon, place 3 to 4 donuts into the oil. Allow to fry on each side, around 40 seconds or until golden brown. Remove from oil and place onto a plate lined with paper towel. Once excess oil has been removed, place donuts on a drying rack to cool.
When all the donuts have been fried and cooled, begin to fill.
Fill pastry bag with prepared vanilla pudding. If you don’t have a tip, you can just snip the corner of the pastry bag with a scissor.
Using a wooden skewer or toothpick, make a hole in the side of each doughnut. Fit the pastry tip into a hole, pipe about 2 to 3 tablespoons worth of pudding in each donut. Repeat with remaining donuts.
In a medium bowl, whisk together confectioners sugar, rum, if using, nutmeg and 2 tablespoons eggnog. If the glaze is too thick, add additional eggnog, 1 teaspoon at a time. Dip each donut in the eggnog glaze. Allow to set.
Fresh donuts are best eaten the same day they are fried.
(Shannon Sarna is the editor of The Nosher.)