Place the flour, sugar, powdered milk, salt and softened butter in the bowl of a stand mixer fitted with a dough hook. Crumble in the yeast, making sure it does not touch the salt.
Knead at medium speed, gradually pouring in the water, until smooth, about 6 minutes. The dough should pull away from the sides of the bowl.
On a lightly floured work surface, flatten the dough into a rectangle. Cover with cling film and chill until firm, at least 2 hours.
Ten minutes before you begin working again, place the 250g of chilled butter in the freezer.
On a lightly floured surface, roll out the chilled dough into a rectangle 6mm thick.
Dust the chilled butter with flour. Roll out the butter into a rectangle half the size of the dough. If the butter is soft, roll it out between sheets of parchment paper that has been lightly dusted with flour.
Arrange the dough with a short side facing you. Place the butter on the bottom half of the dough.Fold the top half of the dough over the butter to enclose it completely.
Rotate the dough clockwise 90 degrees, so that an open edge is facing you. Roll out the dough lengthwise into a rectangle 6mm thick.Fold up the bottom third of the dough so it covers one third of the dough. Fold down the top third to meet the edge.
Fold the entire dough in half to make a double turn. Press down lightly so it is smooth and even.
This makes 4 layers of dough. Cover with plastic wrap and chill for 1 hour.
On a lightly floured surface, arrange the dough with an open side facing you and the closed side on the right. Roll out again into a rectangle 6mm thick. Fold the dough in thirds, like a letter. There are now 3 layers of dough. Cover with plastic wrap and chill for 1 hour.
Roll out the dough on a floured surface to a thickness of about 2cm and use a cutter to stamp out 16 8cm rounds. Then in the middle of each circle, use a 1cm cutter to make them into a doughnut shape.
Place the ring doughnuts on a baking tray lined with greaseproof paper and leave them somewhere warm to prove until doubled in size (around 2 hours).
While the dough is proving, use this time to make the creme patissiere, combine the sugar and corn flour in a medium bowl and add the egg yolks. Whisk just until the sugar is combined, do not let it get too pale, add the lime juice.
Bring the milk to a boil and then whisk a third of the milk into the egg mixture to loosen it.
Whisk in the remaining milk and return the mixture to the saucepan, cook over a medium heat, whisking constantly.
As soon as the pastry cream begins to thicken, remove it from the heat and whisk in the butter until smooth. Stir in the gin.
Scrape the pastry cream into a bowl and cover with a layer of clingfilm, pressing it down so it touches the surface of the cream. This will stop a skin forming, place the creme patissiere in the fridge and allow to cool completely.
By now the doughnuts will have proved, before you start frying, get a bowl of caster sugar ready and some kitchen roll and place it on top of a cake rack. Heat a deep pan of oil (you'll need at least 1 litre of oil) to 180C and add two doughnuts at a time, cooking them for 2 minutes on each side, then using a slotted spoon place the doughnuts on a wire rack covered in kitchen roll. When they are cool enough to touch, roll the sides in sugar.
Continue to cook all the doughnuts, making sure the oil stays at 180C the entire cooking time (you may need to tweak the heat for this) and dusting the sides in caster sugar.
Once the doughnuts are all cooked, leave them to cool and then poke four holes in the bottom of them with a skewer or chopstick. Put the creme patissiere in a piping bag and fill the four holes with the creme patissiere.
To make the glaze sift the icing sugar into a bowl, mix it to a thin consistency with the gin, tonic water and lime juice.
Using a spoon drizzle the glaze over the top of the cakes and then decorate them with a piece of candied lime.
These will keep for a couple of days, but they are best eaten on the day you make them.