Place a rack in the middle of the oven and preheat it to 180 °C / 350 °F. Grease a 26 cm (11-inch) springform pan.
Take the butter from the fridge 30 minutes before making the cake to get it to room temperature. Beat the butter and sugar in a bowl until creamy, for about 2 - 3 minutes. Add one egg at a time, beating well after each addition. Add the vanilla paste and sour cream and mix to combine. Add the flour, baking powder, baking soda, and a pinch of salt. Beat to combine, but don't overwork the mixture. Using a spatula, gently stir in the blackberries. Use fresh or frozen (don't thaw beforehand). Spread the batter into the prepared pan and set aside.
Clean the paddle attachment and beat the cream cheese and sugar until creamy and combined. Using your spatula, spread evenly over the cake.TipWe love using Philadelphia cream cheese for desserts.
Add sugars, ground almonds, flour, and cinnamon powder to a bowl. Cut the cold butter into small cubes. Using your fingertips, lightly rub the butter into the mixture to get a sand-like texture, then knead it together to combine. Sprinkle evenly over the cream cheese mixture.
Bake the cake for 55 - 60 minutes or until the crumble on top is golden brown and the cake is baked. Halfway through baking (25 - 30 minutes), place a piece of aluminum foil over the cake to prevent over-browning. Before taking the cake from the oven, insert a toothpick into the cake. It should come out mostly clean (a few traces of cream cheese mixture are okay). Leave the cake to rest for 30 - 60 minutes at room temperature, then cut into slices and serve.