Make the Dough:
In a small bowl, mix warm milk and yeast. Let sit for 5 minutes until frothy.
In a large mixing bowl or stand mixer, combine flour, sugar, salt, eggs, butter, and yeast mixture. Mix until a smooth, elastic dough forms (about 7–10 minutes).
Place dough in a greased bowl, cover, and let rise for 1–2 hours until doubled in size.
Prepare the Pastry Cream:
In a saucepan, heat milk over medium heat until warm.
In a bowl, whisk sugar, egg yolks, and cornstarch until smooth.
Slowly add warm milk to the egg mixture, whisking constantly. Return to the saucepan and cook over medium heat, stirring, until thickened.
Remove from heat, stir in vanilla extract and butter. Cool and refrigerate until ready to use.
Shape and Fry the Donuts:
Roll out the dough on a floured surface to about ½-inch thickness. Cut into circles using a cookie cutter. Place on parchment paper and let rise for 30 minutes.
Heat oil in a deep fryer or frying pan to 350°F (175°C). Fry donuts in batches for 1–2 minutes per side until golden brown. Transfer to a cooling rack.
Fill the Donuts:
Once cooled, use a piping bag with a small tip to fill each donut with pastry cream.
Make the Chocolate Glaze:
In a small saucepan, heat heavy cream until steaming. Remove from heat and pour over chocolate chips and butter in a bowl. Stir until smooth.
Glaze the Donuts:
Dip the top of each donut into the chocolate glaze and let set on a cooling rack.
