Once all elements have been made and cooled off, it's time to assemble.
Cut the cooled vanilla cake in half to create two rectangles that are 9" x 6.5". Then cut each of those into two layers.
Take one piece of cake as a guide and use a serrated knife to cut the pastry into 4 rectangles of the same size. Save the scraps!
Remove the plastic from the surface of the pastry cream. Use a whisk or a hand mixer to beat until smooth.
Rinse out the 9"x13" pan we used to bake the cake. Line half of the pan with parchment paper - ideally you want the sheets to stick up a couple inches past the top of the pan. They will flop over for now but we'll stick them to the sides of the cake once it's stacked.
Lay one layer of pastry into the lined side of the pan pressing it into the edge of the pan. Scoop about 3/4 of a cup of pastry cream onto the pastry and use an offset spatula or the back of a spoon to spread the cream carefully over the pastry all the way to the edges.
Scoop about 70 grams of plum butter onto the pastry cream and spread it out, stopping just short of the edges so leaving a border of cream uncovered.
Lay one layer of cake over the plum butter and press down gently. Repeat with the cream and plum butter, using the edges of the pan to keep the cake straight and stable.
Repeat all steps starting with the next sheet of pastry, then cream, plum butter, cake, cream, plum butter - until all the layers have been used up.
Once the last layer of cake is on, scoop any remaining cream over top of the cake and spread it out to evenly cover the top and use any excess to fill in gaps on the side of the cake.
Press the excess parchment onto the sides of the cake and cover the top with a sheet of plastic. Transfer the pan and cake to the fridge to set for at least 24 hours - even 48 is great.