1-Preheat oven to 375 degrees and grease: Preheat oven to 375 degrees and grease a 9×9 baking dish.
2-In a food processor or blender, blend: In a food processor or blender, blend blackberries and sugar until smooth. Set aside (if you do not like seeds, strain the puree through a mesh sieve; if seeds are fine, you can skip this step).
3-In a large bowl, sift together flour,: In a large bowl, sift together flour, sugar, brown sugar, baking powder, and salt. Set aside.
4-In a separate bowl, whisk together egg,: In a separate bowl, whisk together egg, milk, vanilla extract, and melted butter.
5-Make a well in the center of: Make a well in the center of the dry ingredients and pour in the wet ingredients. Stir until just combined. Add in sour cream, and fold gently into the batter, stirring until just combined.
6-To make the brown sugar topping, mix: To make the brown sugar topping, mix brown sugar, flour, and cinnamon together. Cut in the butter and mix until the topping looks like coarse crumbs.
7-Pour half the batter into the prepared: Pour half the batter into the prepared pan, spreading the batter all the way to the edges. Spread the blackberry puree evenly over the batter. Top with remaining batter. Using a knife or toothpick, swirl the puree with the batter, if desired.
8-Spread the brown sugar topping over the: Spread the brown sugar topping over the batter.
9-Bake for 30-35 minutes, or until a: Bake for 30-35 minutes, or until a cake tester comes out clean.
10-Allow to cool before serving: Allow to cool before serving. Enjoy!