Heat milk in a saucepan over medium heat until gently bubbling. In a bowl, whisk together egg yolks, cornstarch, and sugar until smooth. Slowly pour warm milk into the egg mixture while whisking continuously. Strain back into pot and cook on medium heat until thickened, about 3-5 minutes. Remove from heat, whisk in butter and vanilla, transfer to a bowl, cover, and cool.

Combine warm milk, sugar, and instant yeast in a mixing bowl and let sit for 5 minutes until frothy. Mix in egg, flour, and salt. Knead dough for 5-7 minutes until smooth. Place in greased bowl, cover, and let rise until doubled, about 1-2 hours.

Punch down risen dough and roll to 1/2 inch thick. Cut out donuts and transfer to a parchment-lined baking sheet. Cover and let rise for 30-60 minutes.

Preheat oven to 350°F. Bake donuts for 8-10 minutes until golden brown. Cool completely on a wire rack.

Create a small hole in each cooled donut and fill with pastry cream using a piping bag until slightly overflowing.

In a skillet, combine sugar and water over medium-low heat, stirring gently until melted and golden brown, about 5 minutes. Dip tops of each filled donut into caramel and let harden.

Best served fresh paired with coffee or tea. Store leftovers in the fridge, consume within 3 days.