Place a sheet of baking paper on a baking tray and lightly brush it with oil. Lay the sheet of puff pastry on the tray and brush with a little water. Sprinkle with 1 teaspoon sugar, then cover with another sheet of baking paper. Place another baking try on top.
Bake 15 minutes, then remove from the oven and peel off the top sheet of baking paper. Carefully flip the puff pastry over, sprinkle with remaining teaspoon of sugar, cover with baking paper and a baking tray again and bake another 10 minutes.
Place the puff pastry on a cutting board and cut into three equal rectangles (this isn't hard as puff pastry usually comes folded in thirds, just follow the fold marks).
Spread half the pastry cream over one of the pieces and tidy the edges with a butter knife. Lay the second piece of puff pastry on top and spread with remaining pastry cream. Top with the last piece of pastry.
Make the icing by whisking together the icing sugar and about 1 1/2 tablespoons water until smooth. In a separate bowl whisk the cocoa powder with a few drops water to make a paste. Place the cocoa paste into a small plastic bag and snip off one corner to make a piping bag.
Top the vanilla slice with an even layer of icing. Before the icing hardens, pipe 5 lines of cocoa powder vertically across the top. Drag a toothpick through each cocoa line in a zig-zag fashion to decorate.
Let icing harden, cut into five slices and serve!
If you like, cut two of the pastry pieces into 5 equal portions before assembly. This isn't necessary but it makes slicing easier later.