In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a hand-held mixer, beat the cream cheese until smooth. Next, add in the sour cream, granulated sugar, and vanilla extract and continue mixing until well combined and smooth. Add in the eggs one at a time and mix on low until just combined.
Pour the cheesecake filling over the prepared crust and spread it out into one even layer. Spoon the blackberry mixture in different spots on top of the cheesecake filling and gently swirl with a knife.
Bake at 325°F for about 30-35 minutes or until the cheesecake has set up.
Remove from the oven to a wire rack to cool completely. Once cooled, cover tightly and transfer to the refrigerator for 3-4 hours, or overnight, or until fully chilled. Slice into bars and enjoy.