Line an 8x8-inch baking pan with parchment paper, leaving an overhang on two sides for easy lifting. Lightly grease the parchment. Preheat the oven to 350°F (175°C).

In a medium mixing bowl, whisk together melted butter, granulated sugar, and light brown sugar until smooth and glossy, about 1 minute. Beat in eggs and vanilla extract until fully combined and slightly lightened in color.

Sift in cocoa powder, flour, and salt. Stir gently with a spatula until just combined. Fold in chocolate chips or chunks if using.

In a separate bowl, beat softened cream cheese with granulated sugar until smooth and creamy, about 1-2 minutes. Add egg yolk and vanilla extract; mix until well combined and no lumps remain.

In a small bowl, stir together blackberry jam and lightly mashed fresh blackberries (if using). If the jam is thick, microwave it for 10 seconds to loosen.

Pour about 2/3 of the brownie batter into the prepared pan and smooth into an even layer. Drop spoonfuls of the cream cheese mixture on top, then dollop the remaining brownie batter in between. Spoon the blackberry mixture in random spots over the cream cheese layer.

Use a butter knife or the tip of a spoon to gently swirl the cream cheese and blackberry mixtures together in figure-eight motions for a marbled effect. Do not overmix.

Bake on the center rack at 350°F (175°C) for 32-38 minutes, until the edges look set and the center jiggles just slightly. A toothpick should come out with a few moist crumbs.

Let the brownies cool completely in the pan on a rack for about 1 hour. For cleanest slices, chill in the fridge for 30 minutes before cutting. Lift out using the parchment overhang and slice into 16 squares.