Check the instructions on your yeast packet to determine if it needs to be activated in liquid. If so, activate it in a little of the lukewarm milk.

Put the flour, sugar, and yeast in the mixer bowl and stir to combine.

Scatter cubes of butter over the flour. Pour in the eggs, lukewarm milk, vanilla, and salt.

Attach a dough hook to the mixer and knead on low speed for 10 minutes until the dough is smooth, elastic, and slightly tacky.

Tip the dough onto a clean work surface and shape it into a smooth ball by kneading it 2-3 times.

Place the dough in a lightly greased bowl and cover with plastic wrap. Leave to prove for 2-3 hours or until tripled in size.

Once risen, tip the dough onto a clean work surface, knock out the air, and knead it a few times into a smooth ball.

Flatten the dough and roll it into a rectangle about ? inch thick.

Use a cookie cutter or glass to cut out round doughnuts about 3.5 inches in diameter. Cut scraps into shapes or re-knead to cut more doughnuts.

Place cut doughnuts on a surface lined with baking parchment and cover loosely with plastic wrap. Leave to prove for 1-1.5 hours until tripled in size.

While doughnuts are proving, make the pastry cream (if using) and let cool.

Heat oil in a large deep pan or pot until it reaches 170?C/337?F.

Cut parchment paper into squares for each doughnut. Carefully drop doughnuts into oil and remove the parchment paper.

Fry doughnuts for 2 minutes, turn over, and fry for another 2 minutes.

Remove and drain on kitchen paper for about 2 minutes then roll in sugar. Let cool before filling.

To fill the doughnuts, insert a small knife into the side and create an incision.

Fill a piping bag with the pastry cream or filling and pipe into the doughnuts.

Serve immediately or store in plastic containers for 1-2 days.