For the puff pastry, put the flour in a mixing bowl. Add the butter, water and salt in order and knead with a hand mixer (dough hook) until smooth. Wrap in plastic wrap and chill for about 20 minutes.
For the butter brick, dice the butter. Sift the flour over it, knead it in with your hands and form the mixture into a brick. Chill the butter brick for about 20 minutes.
Roll out the dough on a floured work surface into a rectangle (approx. 20 x 30 cm) and place the butter brick in the center. Fold the remaining dough over the butter brick so that it is completely “wrapped”. Roll out the dough again into a rectangle. Double up from the narrow side – this should create 3 layers of dough (“easy tour”). Wrap the dough package in plastic wrap and chill for another 20 minutes. Repeat this rolling out technique three more times, always chilling the dough in between.
For the filling, mix jam with rum until smooth.
Roll out the finished dough into a rectangle on a floured work surface, cut into squares and brush the edges of the dough with beaten egg. Place a spoonful of filling on each of the dough pieces and fold them into triangles. Cut a slit in the top center of each triangle, brush the surfaces with egg and sprinkle with cinnamon sugar.
Place the triangles on baking paper and bake at 200 °C hot air in the middle of the oven for about 12 minutes.