Prepare the Pan: Preheat the oven to 350°F and line an 8×8-inch metal baking pan with parchment paper, then grease the lined pan.
Combine Butter, Cocoa, Sugar: Melt the butter in a large microwave-safe bowl for 60–90 seconds on high power, then stir in the cocoa powder and granulated sugar until the mixture is well combined, the sugar is dissolved, and no cocoa lumps remain.
Add Eggs, Vanilla: Add the room-temperature eggs one at a time, mixing after each addition, then stir in the vanilla extract.
Finish the Batter: Gently fold in the flour and salt by hand just until no streaks of flour remain, taking care not to overmix.
Add Chocolate, Blackberries: Fold the chocolate chips and half of the blackberries into the brownie batter until they are evenly distributed.
Fill the Pan: Transfer the batter to the prepared 8×8-inch pan and spread it into an even layer, then arrange the remaining blackberries over the top.
Bake the Brownies: Bake at 350°F for 30–35 minutes, or until the center is just set and a tester inserted into the brownies comes out with moist, fudgy crumbs rather than completely clean.
Cool Before Cutting: Allow the brownies to cool completely in the pan before cutting into squares; for cleaner, neater pieces, refrigerate them before slicing.