Wash the limes and grate them dry. Finely grate the zest of 2 limes (use 1 lime for other purposes). Mix lime zest, fat, sugar, vanilla sugar and salt with the whisk of the hand mixer until thick and creamy.
Stir in the eggs one by one. Mix flour and baking powder, sieve onto the fat cream. Stir in together with the yoghurt. Grease the box form (approx. 2 litres content) and dust with flour. Pour in the dough and smooth it down.
Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for approx. 50 minutes. In the meantime squeeze 1 lime. Mix 3 tablespoons lime juice and icing sugar to a smooth glaze.
Take the cake out of the oven and let it rest in the mould for about 10 minutes. Place on a cake rack. Cover with icing and let it cool down. 3. cut lime into slices and decorate the cake with them.
Sprinkle with brown sugar.