Wash 1 lime, grate the peel and cut in half. Squeeze the lime. Mix the fat, 1 cup of sugar, 1 packet of vanilla sugar, poppy seeds, lime zest and half of the juice for about 5 minutes with the whisk of the hand mixer until creamy. Add the eggs one by one and mix well. Mix flour and baking powder and stir in. Pour the dough into a greased springform pan (26 cm Ø), smooth it down and bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for about 20 minutes.
Take out the cake and let it cool down. Soak gelatine in cold water for 10 minutes. Wash and halve 1 lime. Rub the peel off one half and squeeze the juice. Cut the other half into thin slices for decoration. Whip cream until stiff. Mix quark, 1/2 cup of sugar, lime zest and juice of the two half limes. Squeeze the gelatine, dissolve and mix with 3 tablespoons of the quark cream. Stir the gelatine into the quark cream. Fold in the cream. Carefully remove the cake from the mould and the base. Put the cake back into the mould and spread the quark cream on top.
Mix quark, 1/2 cup of sugar, lime zest and juice of the two half limes. Squeeze the gelatine, dissolve and mix with 3 tablespoons of the quark cream. Stir the gelatine into the quark cream. Fold in the cream. Carefully remove the cake from the mould and the base. Put the cake back into the mould and spread the quark cream on top. Smooth and chill for at least 2 hours. Decorate with the lime slices, poppy seeds and chopped pistachios