Preheat oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving overhang.
Melt butter and chocolate in a microwave-safe bowl in 30-second intervals, stirring until smooth.
Whisk sugar into the melted chocolate mixture. Add eggs one at a time, mixing well after each. Stir in vanilla.
Fold in flour, cocoa powder, and salt just until combined—do not overmix.
In another bowl, beat cream cheese and sugar until smooth. Mix in egg and vanilla.
Toss blackberries with sugar and cornstarch. Let sit for 5 minutes.
Spread brownie batter evenly in prepared pan. Dollop cream cheese mixture over top. Scatter blackberries.
Swirl with a knife to create marbled patterns—don’t overdo it.
Bake for 35–40 minutes or until center is just set and a toothpick comes out with a few moist crumbs.
Cool completely in the pan before slicing.