For the Puff Pastry:
Mix 125 grams butter with the flour and salt using your fingers until the mixture resembles breadcrumbs, then cautiously add the water and mix until you have a firm paste. Pat into a square and wrap in plastic film. Leave to rest in the fridge for at least 1 hour before using.
Once rested, roll the paste into a rectangle about 8 millimeters thick, then beat 375 grams of butter between greaseproof paper into a rectangle a wee bit smaller than half the paste rectangle. Lay the butter on the paste, leaving a space at the end. Fold the un-buttered half over the butter and fold the edges over, so you now have butter in a paste package. Pat square, wrap in plastic film, and allow to rest in the fridge for at least 15 minutes.
Roll out into a rectangle in the opposite direction to your initial major fold (each time you roll out the pastry to fold, turn your pastry and roll across the previous direction you rolled, you will have to sprinkle flour on the surface of your rolling pin - it is very important to dust the flour off the paste before folding it at every turn in the process). Once the pastry is approximately l centimeters to 1½ centimeters thick, fold like a traditional letter, with one end of the rectangle to the halfway mark, and the other end over this. Pat square and place in the fridge for at least 15 minutes to rest again. Repeat this process two more times. Return to the fridge and rest for 1 hour or more.
For the Filling:
Melt the butter and sugar together, then add them to the currants, allspice, and nutmeg. Mix well and leave to cool.
To Assemble and Serve:
Preheat oven to 350°F. Roll the Puff Pastry out to 8 millimeters thick and cut circles approximately 9 centimeters in diameter. On half of these spoon a blob of your Filling in the center of the circle, then place the other Puff Pastry circles on top. Pinch the edges together, gently press to flatten the cakes, then slash the top 3 times.
Paint the top with the egg white, then dip it into the sugar. Bake cakes for 15 to 20 minutes in oven; keep an eye on them so they don't burn.