Defrost the frozen puff pastry in 30-60 min. Roll out the puff pastry on a floured work surface to a 30x30cm sheet. Cut 9 squares from the pastry sheet, each with sides 10cm long.
Mix the hazelnuts with the egg, sugar and rum. Form a strip of nut filling in the center of each pastry square. Brush one side of each pastry square with beaten egg yolk, fold over the opposite side, score at even intervals and pull the incisions apart a little to form a ridge.
Rinse a baking sheet with cold water. Place the nut crests on it with enough space between them and brush their surface with beaten egg yolk. Let the pastry rest for 15 minutes.
Bake in the oven (preheated to 230 G) for 15-20 min. and cool.