1. Prepare the yeast by combining it with warm water and letting it sit for about 10 minutes until it becomes foamy.
2. In a stand mixer, mix together the flour, sugar, and salt. Slowly add the yeast mixture.
3. Gradually incorporate eggs into the dough, mixing thoroughly after each addition.
4. Add room temperature butter, lemon zest, and vanilla extract (if using) to the dough and knead until smooth and elastic.
5. Allow the dough to rest by refrigerating it overnight or letting it sit at room temperature for a few hours until it doubles in size.
6. Once risen, divide the dough into equal parts. Shape into small buns by rolling the dough in your hands.
7. Place the shaped buns on a tray lined with parchment paper, cover with a towel, and let rise again until doubled in size.
8. Heat oil in a deep fryer or pot to 175°C/350°F. Fry the doughnuts in small batches, ensuring each side cooks for about 2 minutes until golden brown.
9. After frying, drain the doughnuts on a paper towel-lined plate.
10. Make the pastry cream by heating milk in a saucepan until hot but not boiling.
11. In a separate bowl, whisk egg yolks, sugar, and cornstarch.
12. Slowly add the hot milk to the egg mixture while whisking constantly, and then return the mixture to the saucepan. Cook on medium heat until thickened.
13. Remove from heat, stir in butter, and let the pastry cream cool to room temperature. Transfer the cream to a piping bag.
14. Pipe the cooled pastry cream into the fried doughnuts through a small hole.
15. Prepare the caramel topping by caramelizing sugar with a kitchen torch or using the wet caramel method (heating sugar with water until golden brown).
16. Dip the doughnuts in the caramel mixture and allow the caramel to harden, forming the signature crunchy layer.
17. Serve and enjoy the combination of soft doughnut, creamy filling, and crispy caramel topping.