Melt 30g brown sugar and 30g butter together in a saucepan over medium heat. Add blackberries to brown sugar mixture; cook and stir until mixture bubbles, 1 to 3 minutes. Stir 150g caster sugar into berries, crush berries slightly with a fork and continue cooking until berries are hot and slightly broken-down, about 5 minutes more; remove from heat and pour into a 23cm cake tin.
Beat 200g caster sugar and 120g butter together in a bowl with an electric mixer until light and fluffy; beat in eggs.
Whisk flour, baking powder and salt together in a bowl. Alternately stir flour and milk into butter mixture, beginning and ending with the flour mixture. Mix vanilla into cake batter.
Pour cake batter over blackberry mixture in the cake tin.
Bake cake in the preheated oven until cooked through, 35 to 40 minutes. Let cake cool in the pan until warm, but not completely cooled, about 30 minutes. Run a knife along the inside edge of the baking tin to separate cake from the sides; place a cake serving plate over the top of the tin and flip the tin. Lift the tin slowly to release the cake.