Wash, halve and stone the apricots and cut them into wide slices. Carefully wash the currants and remove them from the panicles with a fork. Grease a fat pan (deep baking tray; approx. 32 x 39 cm) well.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer).
For the dough mix 450 g flour, baking powder, 125 g sugar, vanilla sugar and 1 pinch of salt. Add milk, oil, egg and quark and knead until smooth with the dough hooks of the mixer. Roll out the quark and oil dough on the fat pan.
Press on edges and corners with floured hands.
Spread 75 g butter in flakes on the dough. Add the apricots and currants. Bake the cake in a hot oven for 30-35 minutes. Remove and let cool on a cake rack.
For the pesto, wash lime hot, dab dry and rub the peel. Squeeze the lime. Crush the pistachios, lime zest and 1 tbsp. sugar in a universal chopper or chop with a large kitchen knife.
Stir in the juice. Cut the cake into pieces and dust with icing sugar. Add the pistachio pesto.