In a small saucepan, combine the frozen blackberries, sugar, lemon zest, and lemon juice. Cook over medium-low heat, stirring occasionally, until the berries soften and release their juices, about 8 to 10 minutes.

Place a fine-mesh sieve over a bowl and pour the berry mixture through it. Use the back of a spoon or spatula to press the mixture through the sieve, collecting as much liquid as possible. Discard the seeds and solids.

Pour the strained juice back into the saucepan and set it over low heat. In a small bowl, stir together the cornstarch and water until smooth. Add this mixture to the blackberry juice and cook, stirring constantly, until the sauce thickens slightly, about 1 to 2 minutes. Remove from the heat and allow the sauce to cool completely. To speed things up, you can place it in the refrigerator.

Preheat the oven to 350 degrees F. Line an 8-inch square baking pan with parchment paper, leaving a bit of overhang on the sides so the brownies can be lifted out easily later.

In a large bowl, whisk together the melted butter, brown sugar, and salt until smooth. Add the egg, egg yolk, and vanilla extract, whisking until fully combined.

Add the cocoa powder, flour, and baking soda. Stir just until the batter comes together and no dry streaks remain. Spread the batter evenly into the prepared pan.

In a medium bowl, beat the cream cheese, sugar, salt, and nutmeg with an electric mixer until smooth and creamy. Add the egg white, lemon juice, and vanilla extract and mix until well blended.

Pour in the whipping cream and mix just until incorporated. Spread the cheesecake mixture gently over the brownie batter.

Spoon the cooled blackberry sauce over the cheesecake layer. Use a knife or skewer to swirl the sauce through the cheesecake layer, creating a marbled pattern while leaving the brownie base mostly undisturbed.

Bake for 55 to 60 minutes, or until the center is mostly set and lightly puffed. The edges may rise slightly higher and begin to turn golden.

Allow the brownies to cool completely in the pan. Once cooled, refrigerate for at least 4 hours or overnight before slicing.