Preheat oven to 350°F (177°C). Grease a 9-inch or 10-inch springform pan.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter and 3/4 cup granulated sugar together on high speed until creamy and combined, about 3 minutes. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) On medium speed, add 1 egg at a time, beating well after each addition. Beat in the vanilla extract and sour cream. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. Add the flour, baking powder, baking soda, and salt. Turn the mixer on low speed and beat until completely combined. Using a rubber spatula or wooden spoon, fold in the blackberries. Batter is thick.

Spread the batter into the prepared pan. Set aside.

Using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and remaining 1/4 cup granulated sugar together until creamy and combined. Spoon and spread over cake batter. It’s a thick cream cheese topping, so do your best to spread around—doesn’t have to be perfect.

Combine the brown sugar, flour, and cinnamon together in a medium bowl. Cut in the cold butter with a pastry blender or a fork (or even with your hands) until the mixture resembles pea-sized crumbs. Sprinkle evenly over cream cheese layer.

Bake the cake for 60-65 minutes or until it no longer jiggles in the center. A toothpick inserted in the center should come out *mostly* clean. (A few moist crumbs are fine.) Halfway during bake time (about 30 minutes), tent a piece of aluminum foil over the cake to help prevent over-browning around the edges.

Cool cake for at least 30 minutes before removing the sides of the springform pan and slicing and serving. During this time, you can make the icing by whisking the icing ingredients together until smooth. Add more milk/cream/lemon juice to thin out if needed. Drizzle icing over cake while it’s still warm.

Cover and store leftover cake at room temperature for up to 1 day or in the refrigerator for up to 5 days.