1. In a small bowl, whisk together yeast, 1 tablespoon of the sugar, and 1/2 cup warm water until yeast is dissolved. Let stand for 10 minutes.
2. In a large food processor, combine flour, milk, egg, egg yolk, salt, yeast mixture, and remaining 2 tablespoons sugar. Cover and process until combined. Add butter; cover and process until combined (dough will be sticky).*
3. Place dough in lightly greased bowl; cover and chill in refrigerator overnight (8 to 12 hours).
4. On a well-floured surface, roll dough to 1/2-inch thickness. Using a 2-1/2-inch round cutter, cut dough. Reroll as necessary. Arrange dough rounds on a baking sheet dusted with all-purpose flour. Cover and let rise about 30 minutes or until nearly double in size.
5. Heat 2 inches of oil in a deep saucepan to 365 degrees F. In a bowl, place 1/3 cup sugar; set aside. Place chocolate-hazelnut spread in a decorating bag fitted with a large round tip; set aside.
6. Fry doughnuts, three at a time, in deep hot oil about 2 minutes on each side or until golden brown. Remove doughnuts using a slotted spoon; drain on paper towels. While warm, use tongs to dip each doughnut in sugar to coat. Holding each doughnut (use tongs if necessary), use a dowel, chopstick, or prong of an instant-read thermometer to poke a hole in one side of doughnut. Pipe chocolate-hazelnut spread through opening. Repeat on opposite side of doughnut. Serve warm. Makes about 16 doughnuts.
*Chill dough overnight!