Check the instructions on the yeast packet. If it needs activation, dissolve it in a little lukewarm milk.

In a mixer bowl, combine the flour, sugar, and yeast. Scatter cubes of butter over the mixture.

Add the eggs, lukewarm milk, vanilla, and salt to the bowl.

Knead with a dough hook attachment on low speed for 10 minutes until the dough is smooth, elastic, and slightly tacky.

Tip the dough onto a clean, unfloured surface and shape it into a ball. Place in a lightly greased bowl and cover with plastic wrap. Leave to prove for 2-3 hours or until tripled in size.

After the dough rises, knock out the air and knead a few times to form a smooth ball.

Roll out the dough to a ½ inch thick rectangle. Cut out rounds about 3.5 inches in diameter.

Place the cut doughnuts on parchment-lined surfaces, cover loosely with plastic wrap, and leave to prove for 1-1.5 hours or until tripled in size.

Prepare the pastry cream while the doughnuts are proving.

Heat oil in a large pan or pot to 170°C/337°F. Cut parchment into squares for each doughnut.

Carefully drop the doughnuts into the oil, removing the parchment paper. Fry in batches, do not overcrowd.

Fry for 2 minutes, turn over, and fry for an additional 2 minutes. Drain on kitchen paper for around 2 minutes.

Roll the warm doughnuts in sugar and let them cool before filling.

To fill, insert a knife into the side, making a small incision.

Fill a piping bag with pastry cream and pipe it into the doughnuts. Serve immediately or store in plastic containers for 1-2 days.

For the pastry cream, whisk together egg yolks, sugar, vanilla, and lemon zest.

Add cornstarch and whisk until combined.

Heat milk in a saucepan until hot, then pour it slowly into the egg mixture while whisking continuously.

Return the mixture to the saucepan and heat on low, stirring constantly until thick and creamy (about 10-15 minutes).

Once thick, pour into a clean bowl and cover with plastic wrap to cool.