Preheat oven to 350°F (175°C) and grease a 9x9-inch baking pan or line it with parchment paper. In a microwave-safe bowl, melt the 1/2 cup unsalted butter with 1 cup dark chocolate chips until smooth, stirring every 20 seconds to avoid burning. Stir in 1 cup granulated sugar while warm. Let cool slightly, then mix in 2 eggs and 1 teaspoon vanilla extract thoroughly.
Sift together 1/2 cup all-purpose flour and 1/4 teaspoon salt. Gently fold into the chocolate mixture just until combined, careful not to overmix. Batter should be thick and glossy.
In a clean mixing bowl, beat 8 ounces softened cream cheese until smooth. Add 1/4 cup powdered sugar and 1/2 teaspoon vanilla extract, mixing until fully incorporated and fluffy. This is the cheesecake layer.
Pour half of the brownie batter into the prepared pan and spread evenly. Dollop the cheesecake mixture over the brownie layer in spoonfuls. Sprinkle 1 cup fresh blackberries evenly over the cheesecake layer, gently pressing some in but leaving most on top. Spoon remaining brownie batter over top, then swirl gently with a knife or skewer to create a marbled effect.
Bake for 35-40 minutes until edges are set and a toothpick inserted near the center comes out with a few moist crumbs. Cool completely in the pan on a cooling rack before slicing into squares.