Pour milk into a medium sized saucepot, set over medium heat until steaming and edges bubble. Remove from heat.

In a medium bowl, whisk together egg yolks, sugar, and cornstarch until smooth. Gradually pour hot milk over the egg mixture while whisking.

Strain the mixture back into the saucepot and cook over medium heat, whisking constantly until it thickens to a soft pudding consistency (5 to 10 minutes).

Remove from heat, whisk in butter and vanilla. Pour into a heat-safe bowl, cover with plastic wrap touching the surface, and chill in the fridge for 1 to 2 hours.

Warm milk until warm to the touch (not hot). In a large bowl, whisk warm milk, 1 tablespoon sugar, and yeast. Let sit for 5 to 10 minutes until bubbly.

Add remaining sugar, egg, vanilla, and butter; whisk to combine.

Mix half the flour with the wet ingredients, then add remaining flour and salt. Mix until it forms a ball of dough.

Turn dough onto a floured surface and knead for 5 to 10 minutes until smooth and elastic.

Oil a large bowl, place dough inside, cover, and let rise in a warm place for 45 minutes to 1 hour until doubled in size.

Line 2 large baking sheets with parchment paper. Punch down risen dough and roll out to ½ inch thick. Cut donut shapes using a 3-inch cookie cutter.

Arrange donuts on baking sheets with space between them. Cover and let rise in a warm place until doubled in size (30 to 45 minutes).

Preheat oven to 375°F. Uncover donuts and bake for 10 to 12 minutes until puffed and golden brown.

Transfer baked donuts to a wire rack to cool completely before filling.

Use a sharp knife to make a hole in the side of each donut. Fill a piping bag with chilled pastry cream and fill each donut until the cream starts to push out.

Chill filled donuts in the fridge until ready to top with caramelized sugar.

In a medium skillet, combine sugar, water, and salt. Bring to a boil without stirring until it starts to brown, then remove from heat.

Let sit for about 1 minute until the sugar turns amber. Dip the tops of the donuts into the caramelized sugar and place on a wire rack until hardened (5 to 10 minutes).