Melt the butter and chocolate in a small pot at low heat while stirring. Pour the chocolate mixture into a large bowl, add brown sugar, eggs and milk and mix with the whisk of the hand mixer for 2-3 minutes. Add flour, stir again. Spread the dough into a square springform pan (24 x 24 cm) lined with baking paper and bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for about 20 minutes.
In the meantime, mix cream cheese, sugar and starch. Wash the blackberries and dab dry. Finely puree the blackberries with a hand blender. Remove the mould from the oven, spread the cheese mixture on top and swirl the blackberries on the surface with a fork.
Bake the cake at the same temperature for about 40 minutes. Remove, let cool and put in a cool place for about 1 hour. Remove the cake from the tin. Cut into pieces and arrange.