Bloom the Yeast: Mix warm milk, sugar, and yeast in a stand mixer bowl. Let it sit for 5-10 minutes until foamy.
Mix the Dough: Add flour, egg yolks, and salt. Use the dough hook on low speed until combined.
Incorporate Butter: Increase speed to medium. Add softened butter one tablespoon at a time, allowing each to incorporate before adding the next. Knead for 5-7 minutes.
First Rise: Place dough in a greased bowl, cover with plastic wrap, and let rise in a warm spot for 60-90 minutes (until doubled).
Make Pastry Cream: While dough rises, whisk egg yolks, sugar, and cornstarch. Heat milk and vanilla until simmering. Temper the eggs with hot milk, return to heat, and whisk until thick.
Chill Filling: Strain the custard through a sieve, stir in butter, and cover with plastic wrap (touching the surface). Chill for 4 hours.
Shape: Roll dough to 3/4 inch thickness. Cut circles and place on parchment squares.
Second Rise: Cover and let rise for 30-45 minutes until puffy.
Fry: Heat oil to 350°F. Fry donuts for 2 minutes per side until golden. Drain on paper towels.
Fill: Once cool, poke a hole in the side, and pipe in the chilled pastry cream.
Glaze: Heat cream and chocolate until smooth. Dip the tops of the filled donuts into the glaze.