1. Make the Dough

• In a small bowl, combine warm water (or milk) and yeast. Let sit for 10 minutes until foamy.

• In a stand mixer with the dough hook, mix flour, sugar, and salt. Add the yeast mixture and mix to combine.

• Add eggs one at a time, mixing thoroughly after each addition.

• Add the butter, vanilla, and lemon zest (if using). Knead for 8–10 minutes until the dough is smooth and elastic.

• Cover and let rise in a warm spot until doubled in size (1–2 hours), or refrigerate overnight.

2. Shape and Fry

• Divide the risen dough into 12 equal portions and roll into balls.

• Place on a parchment-lined tray, cover, and let rise again for about 30–45 minutes, until puffy.

• Heat oil in a deep fryer or pot to 175°C (350°F).

• Fry in batches for 2 minutes per side, or until golden brown. Drain on paper towels.

3. Make the Pastry Cream

• Heat the milk in a saucepan until hot but not boiling.

• In a separate bowl, whisk together egg yolks, sugar, and cornstarch.

• Slowly whisk in the hot milk, then return the mixture to the saucepan.

• Cook over medium heat, whisking constantly until thickened.

• Remove from heat, stir in butter and vanilla (or other flavorings).

• Let cool to room temperature, then transfer to a piping bag.

4. Fill the Doughnuts

• Use a skewer or knife to make a small hole in each doughnut.

• Pipe cooled pastry cream into each doughnut until filled.

5. Caramelize the Tops

• Sprinkle a thin, even layer of sugar on top of each filled doughnut.

• Use a kitchen torch to melt the sugar until golden and crisp.
  Alternatively: Dip doughnut tops into caramel made using the wet method (heat sugar with a bit of water until golden), then set aside to harden.