Prepare the Dough:

1. Bloom the Yeast: In a small bowl, combine the warmed milk and yeast. Let it sit for 5-10 minutes until foamy.
2. Mix the Wet Ingredients: In a large bowl, beat the eggs and sugar together. Add the yeast mixture and softened butter.
3. Combine with Dry Ingredients: Gradually add the flour and salt. Mix until a soft dough forms.
4. Knead the Dough: Turn the dough onto a floured surface and knead for 8-10 minutes until smooth and elastic.
5. First Rise: Place the dough in a greased bowl, cover with a damp towel, and let it rise in a warm place for 1 hour or until doubled in size.

Prepare the Bavarian Cream:

6. Heat the Milk: In a saucepan, heat the milk over medium heat until it just begins to simmer.
7. Mix the Yolks and Cornstarch: In a separate bowl, whisk together the egg yolks, sugar, and cornstarch until smooth.
8. Temper the Eggs: Gradually add the hot milk to the egg mixture while whisking constantly.
9. Cook the Cream: Return the mixture to the saucepan and cook over medium heat, stirring constantly, until thickened.
10. Add Vanilla and Butter: Remove from heat and stir in the vanilla extract and butter. Let the cream cool completely.

Shape and Fry the Donuts:

11. Roll Out the Dough: Roll out the dough to ½-inch thickness on a floured surface. Cut out circles using a donut cutter or a 3-inch round cutter.
12. Second Rise: Place the dough rounds on a parchment-lined baking sheet. Cover and let rise for 30 minutes.
13. Fry the Donuts: Heat the oil to 350°F (175°C). Fry the donuts in batches for 1-2 minutes per side until golden brown. Drain on paper towels.

Fill and Finish the Donuts:

14. Fill with Bavarian Cream: Once the donuts are cool, use a piping bag fitted with a round tip to fill each donut with Bavarian cream.
15. Dust or Glaze: Dust with powdered sugar or dip the tops in chocolate glaze if desired.