In a saucepan over medium heat, combine blackberries, sugar, and lemon juice. Cook until the blackberries break down and the mixture thickens, about 5-7 minutes. Remove from heat and let cool slightly.

Preheat the oven to 350°F (175°C) and grease an 8x8 inch baking pan.

In a mixing bowl, whisk together the melted butter and sugar until smooth. Add the eggs and vanilla, mixing until well combined.

Sift in the cocoa powder, flour, salt, and baking powder. Stir until just combined.

Pour half of the brownie batter into the prepared pan, spreading it evenly.

Spoon the blackberry mixture over the batter, then dollop the remaining brownie batter on top. Use a knife to swirl the blackberry mixture into the brownie batter.

Bake in the preheated oven for 25 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.

Allow to cool in the pan before cutting into squares.