1. Prepare the tangzhong by cooking flour and water into a thick paste, then let it cool.
2. Make the dough by mixing flour, sugar, yeast, salt, and the cooled tangzhong.
3. Add egg yolks, warmed cream, and melted butter, then knead until smooth and elastic.
4. Let the dough rise in a warm place for about 1.5 hours until doubled in size.
5. Roll out the dough to about ½ inch thick and cut into rounds.
6. Place dough rounds on a baking sheet, cover, and let rise for about 45 minutes.
7. Bake at 350°F for around 10 minutes or until golden brown.
8. While the doughnuts cool, prepare the pastry cream by heating milk and vanilla until warm.
9. Whisk egg yolks, sugar, and cornstarch, then slowly add the warm milk while whisking.
10. Return the mixture to the heat and cook until thickened, then cool completely.
11. Fill a piping bag with the cooled pastry cream and use a filling tip to inject it into each doughnut.
12. Make the caramel topping by cooking sugar and water until golden brown.
13. Carefully spoon or dip the tops of the doughnuts into the caramel.
14. Let the caramel cool and harden to form a crisp brûlée shell.
15. Serve immediately for the best texture and flavor.