Sort the blackberries. Grease a bundt pan thoroughly.
Mix the flour and baking powder. Cut the vanilla pod lengthways and scrape out the pulp. Put the butter, a pinch of salt, sugar and the vanilla pulp in a bowl and beat until frothy for at least 5 minutes. Stir in eggs one at a time for 1/2 minute. Add flour and milk alternately and stir in quickly.
Alternately fill the batter with the blackberries in the baking pan. Bake in the hot oven at 175 ° (convection 160 °) on the grid in the lower third of the oven for about 50 minutes.
Let the cake cool for 10 minutes in the tin, then turn it out onto a wire rack.
Mix the powdered sugar and lemon juice to a smooth glaze and spread over the cake.