For the nut buns with lemon glaze, mix walnuts with butter, sugar, cinnamon and rum to a spreadable mass. Roll out the puff pastry slightly larger with a rolling pin, spread thickly with the nut filling and roll up.
Cut 2-3 cm thick slices from the roll and lay flat on a baking tray covered with baking paper. Preheat the oven to 180 °C. Beat the egg and brush the snails with it.
Bake in the oven for about 25 minutes. Squeeze the lemon and mix with the powdered sugar to a thick, spreadable mass. Coat the snails with the glaze as soon as they come out of the oven and let the nut snails with lemon glaze dry.