In the stand mixer fitted with the dough hook, combine the yeast and milk. Allow the yeast to dissolve, about 1 minute. Add the flour, 1/3 cup of the sugar, salt, and eggs and mix on low for about 4 minutes to develop the dough. Begin adding the butter, one piece at a time, and continue mixing for 5 to 6 minutes.
Remove the dough from the bowl and tightly wrap in plastic wrap. Refrigerate for 6 - 15 hours.
Lightly flour a baking sheet. Flour your work surface and roll out the dough into a 12 inch square about a 1/2 inch thick. Using a 3 1/2 to 4 inch round biscuit cutter, cut out the donuts. (I ended up with 11 total.) Arrange the donuts on the prepared baking sheet and cover in plastic wrap. Allow to rise in a warm spot for 2 - 3 hours or until doubled in height and feel poufy and pillowy.
When ready to fry, heat 3 inches of oil in a heavy pot to 350 degrees. Line a try with paper towels and add the remaining 1 cup of sugar in a small bowl. Add the donuts to the hot oil, being careful not to crowd the pan, and fry on each side until golden brown, about 2-3 minutes per side. Remove from the oil with a slotted spoon and allow to drain on the lined tray. When cool enough to handle, toss in the sugar to coat. Return each donut to the tray to cool completely, about 3o minutes.
Fill a pastry bag fitted with a small round tip with Nutella. Poke a hole in the donuts equidistant between the top and bottom and squirt in about 1/3 cup of Nutella. Serve immediately.