The day before make the filling. Mix the nog and sugar in a pot and bring to a simmer. Remove from heat. Whisk the yolks, egg, cornstarch, and sugar in a bowl. Drizzle the hot nog mixture into the eggs while whisking. Then add it all back to the pot over medium heat. Bring to a simmer and watch it thicken up. Remove from heat and whisk in butter, vanilla, and nutmeg. Pour into a bowl and cover with plastic wrap so the plastic touches the surface of the pastry cream. Store in the fridge overnight.
Make the dough- Mix the flour, yeast, sugar, and salt. Pour in the milk and melted butter. Stir to combine. Add in the egg and yolk and continue to stir. Pour on to the counter and knead for about 7 minutes until smooth to the touch. (you could also do this in a stand mixer) Put into a greased bowl covered with plastic wrap and allow to rise for 2 hours or until at least doubled in size.
Roll out the dough to about a half inch thin and cut out donut rounds. Place on a floured surface and brush with melted butter. Cover and allow to rise about an hour.
Bring oil to 350 and fry the donuts in batches, about 1 or 2 minutes per side. Remove from oil to a paper towel or drying rack.
Use a knife to make a hole in the side of the donuts and create a cavity in the center.
Use a piping bag to pipe the pastry cream into the donuts.
Mix the powdered sugar with the milk and whiskey until it reaches the desired texture, adding more sugar if needed.
Glaze the top of the donuts and add the sprinkles on top.