In a salad bowl, mix the almond powder, sugars, cinnamon and melted butter. Gradually add the orange blossom water to obtain a smooth but not liquid paste; it must be spooned.
Cut the pastry sheets into quarters.Place a small spoonful of the almond mixture on the baking tray. Continue rolling the brick sheets into cigar shapes. To do this, fold the corner over the dough, then the right and left edges. Roll well and wet the edges with the egg white to seal the cigars.
Heat the oil in a pan and place the cigars in it for 2 to 3 minutes, until they are nicely browned on all sides.
At the same time, you can prepare the syrup. In a saucepan, gently heat the honey and orange blossom water until they thicken a little.
At the end of cooking, place the cigars on absorbent paper for a few seconds and pour the syrup over the still hot cigars.
Arrange the cigars on a rack and wait a few minutes before enjoying them.