Berliners (Jelly-Filled Donuts)

Combine yeast and milk in a bowl; let sit until foamy, about 10 minutes. Beat 1⁄2 cup sugar and butter in a stand mixer fitted with a paddle attachment until fluffy. Add yeast mixture, vanilla, salt, egg, and yolks; beat until combined. With the motor running, slowly add flour; beat until dough is smooth. Transfer to a lightly greased bowl and cover loosely with plastic wrap; set in a warm place until doubled in size, about 1 1⁄2 hours.

On a lightly floured surface, roll dough into a 14" round about 1⁄2" thick. Using a floured 3" ring cutter, cut dough into 20 rounds; gather and reuse scraps. Transfer rounds to lightly greased parchment paper—lined baking sheets, at least 3" apart. Cover loosely with plastic wrap and set in a warm place until doubled in size, about 30 minutes.

Heat 2" oil in a 6-qt. saucepan until a deep-fry thermometer reads 350°. Using scissors, cut the donuts out of the parchment paper, leaving about 1" of paper around the sides of each donut (the paper makes it easier to transfer them to frying oil). Working in batches, place donuts in oil, paper side up, using tongs to quickly peel off and discard paper. Cook, flipping once, until puffed and golden, 2-3 minutes. Using a slotted spoon, transfer to a baking sheet with a wire rack; let cool completely.

Place remaining sugar in a large bowl; set aside. Fill a pastry bag fitted with a plain 1⁄4" tip with jam. Working with one donut at a time, insert tip about 1⁄2" deep into the side of donut, pipe 2-3 tbsp. jam, and toss generously in sugar.