In a small bowl, combine lukewarm milk, granulated sugar, and active dry yeast. Let sit for 5–10 minutes until frothy.

Whisk together all-purpose flour and salt in a large mixing bowl. Make a well, add yeast mixture, beaten eggs, melted butter, and vanilla extract. Stir until a soft dough forms.

Knead dough on a floured surface for 8-10 minutes until smooth and elastic. Place in greased bowl, cover with a towel, and let rise for 1–1.5 hours until doubled in size.

Heat whole milk and vanilla in a saucepan until simmering. In a separate bowl, whisk egg yolks, granulated sugar, and cornstarch. Slowly add warm milk, return to heat and whisk until thickened. Cool in a bowl covered with plastic wrap.

Punch down risen dough, roll out 1/2 inch thick, cut into circles. Place on floured baking sheet, cover, and let rise for 30-45 minutes until puffy.

Heat oil in pot to 350°F. Fry dough circles in batches for 2-3 minutes each side until golden. Remove and drain on paper towels.

Fill doughnuts with pastry cream using a piping bag, then roll in granulated sugar while warm before serving.