Grease a square springform pan (approx. 24 x 24 cm; alternatively a round one of 26 cm Ø) and dust with flour. Break the chocolate into pieces. Melt it with 250 g butter in a hot water bath, let it cool down a bit.
Mix 5 eggs and 350 g sugar with the whisk of the mixer for about 10 minutes until thick and creamy. Stir in the syrup. Mix flour, baking powder and 1 pinch of salt. First stir the chocolate mixture into the egg mixture and then stir in the flour mixture.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Mix 90 g butter and 130 g sugar with the whisks of the mixer for approx. 5 minutes until creamy. Stir in 3 eggs individually.
Stir in cream cheese by the spoonful.
Smooth the brownie dough in the mould. Spread the cream cheese mixture in patches on the dough and fold it in lightly to create a marbling effect.
Bake in a hot oven for 50-60 minutes, possibly covering with aluminium foil about 10 minutes before the end of the baking time. Take out of the oven and let cool down for about 10 minutes. Remove from the springform pan and let it cool down.