Combine warm milk, yeast, and a pinch of sugar; let stand until foamy.

Whisk in remaining sugar, egg, yolk, melted butter, and vanilla.

Gradually add flour and salt, mixing until a shaggy dough forms.

Knead for 5-7 minutes until smooth.

Place in an oiled bowl, cover, and let rise for 1.5 to 2 hours.

Punch down dough and roll to 1/2-inch thickness.

Cut out 12 donuts.

Place on a parchment-lined sheet, cover, and let rise for 30-45 minutes.

Preheat oven to 350°F (175°C).

Bake for 10-12 minutes.

Let cool completely.

Heat milk until simmering.

Whisk sugar, cornstarch, and egg yolks in a separate bowl.

Temper the egg mixture with hot milk, then return to saucepan and cook until thick.

Strain, stir in vanilla and butter.

Cover surface directly with plastic wrap and chill for at least 4 hours.

Fill cooled donuts with chilled pastry cream using a piping bag.

Dip the top of each filled donut into granulated sugar.

Use a kitchen torch to caramelize the sugar until a hard, amber crust forms.

Serve immediately.