Allow the puff pastry to defrost at room temperature until pliable, about 1 hour.
Preheat oven to 445˚F (230˚C). Line two baking sheets with parchment or lightly grease.
In a large bowl, combine the hazelnuts, sugar, cinnamon salt, rum, and 1 egg. Divide the filling into 9 equal sections. In a small bowl, beat the egg yolk.
On a lightly floured surface, roll the puff pastry into a 12x12 inch (30x30 cm) square. Cut the puff pastry into 9 equal squares, each 4x4 inches (10x10 cm). Place a section of filling in the center of a pastry square and form into a strip down the middle, leaving a 1/2 inch border on the two closest edges and about 1 1/2 inches on the other opposite two sides. Brush the edges of one half of the square with beaten egg yolk. Fold the square over, enclosing the nut mixture and sealing the edges. Using a sharp knife, make slits about 1 inch deep and 1/2 inch apart along the long, sealed edge. Gently pull the pastry side opposite the slits into a slight horseshoe shape to separate the slits, pulling apart any that are sticking together, to form a comb. Transfer the pastry to the prepared baking sheet. Repeat with remaining puff pastry and filling. Brush the tops with the remaining egg yolk and allow to rest for 15 minutes.
Bake in preheated oven until golden brown, 15-20 minutes. Transfer to a wire rack and allow to cool.
If desired, whisk together the powdered sugar and milk. Drizzle over the tops of the Nusskämme or dip the tops in the glaze to coat in a single layer.