Preheat the oven to 200 C / Gas Mark 6.

Lay out a sheet of parchment on a baking tray, lightly brush with oil. Lay the puff pastry sheet over the parchment paper, then brush the top with a little water.

Sprinkle with 1 teaspoon of the sugar, then cover with another sheet of parchment paper and then another baking tray. Press down slightly.

Bake in the oven for 15 minutes. Remove from the oven and carefully peel off the top layer of parchment paper. Flip over the puff pastry sheet, then sprinkle with 1 teaspoon sugar and cover with the sheet of parchment and the baking tray. Press down slightly again.

Bake for another 15 minutes.

Carefully transfer the puff pastry sheet to a cutting board. Cut the sheet into three equal pieces. 

Spread half of the pastry cream over the whole piece of puff pastry. Clean up the edges by running a knife alongside the pastry. Lay the second piece on top, then spread with the remaining pastry cream. Finally, top with the last piece of puff pastry.

Make the icing by whisking together the icing sugar and 1 1/2 tablespoons of water till smooth. In a separate bowl, combine the cocoa powder with a few drops of water and mix till a paste forms. Place the cocoa paste in a piping bag and cut tip to pipe.

Pour a thin, even layer of the icing over the top of the mille feuille. Working quickly so that the icing doesn't harden, immediately pipe 6 thin lines of cocoa paste horizontally across the top . Drag a skewer through the lines of cocoa lengthways to decorate.

Let the icing harden in the fridge before slicing and serving.