Wash the lemon hot, dab dry and finely grate the peel. Put half the rind in a mixing bowl with 375 g flour, sugar, egg, cardamom, 1 pinch of salt and butter in pieces. Knead first with the dough hooks of the mixer, then briefly with your hands to form a dough.
Form into a flat brick. Cover and chill for 1 hour.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Line a baking tray with baking paper. Halve the dough (put the other half back in the fridge). Roll out to a thickness of approx. 4 mm on a floured work surface.
Cut out circles with a wavy edge (à approx. 4.5 cm Ø), knead the dough remains together again briefly, roll out and cut out. Place circles on the baking tray. Bake in a hot oven for about 10 minutes. Remove from the oven and leave to cool briefly on the baking tray.
Pull the paper onto a cake rack and let it cool down. Prepare the second half of the dough in the same way.
For decoration, lightly crush sea salt with the rest of the lemon peel in a mortar. Squeeze the lemon. Stir 3-4 tablespoons of juice with icing sugar to a smooth glaze. Coat the cookies with it.
Spread 1 pinch of lemon salt on each cookie. Let the icing dry.