In a medium saucepan, whisk together egg yolks, sugar, cornstarch, and whole milk over medium heat. Stir constantly until thickened, about 5-7 minutes. Remove from heat, blend in unsalted butter and vanilla extract. Chill in the refrigerator for at least 2 hours.

In a large mixing bowl, combine all-purpose flour, sugar, active dry yeast, and salt. In a separate bowl, mix warm milk, eggs, and melted butter until combined. Pour wet ingredients into dry mix, knead dough on a floured surface for 8-10 minutes until smooth.

Place kneaded dough into a greased bowl, cover with a damp cloth, and let rise in a warm place for about 1 hour.

Once the dough has risen, punch it down, roll it out to ½ inch thickness, cut out donut shapes and holes. Place on a baking sheet, cover, and let rise for another 30 minutes.

Heat vegetable oil to 350°F. Fry donuts until golden brown on both sides, about 2-3 minutes per side. Transfer to paper towels to drain excess oil.

Roll drained donuts in granulated sugar. Fill each donut with chilled Bavarian cream using a piping bag.