01 - Preheat oven to 325°F. Lightly grease a 9-inch springform pan and line the base with parchment paper.
02 - Combine crushed graham crackers, melted butter, and sugar in a bowl. Press mixture evenly into the base of the prepared pan. Bake for 8 minutes, then set aside to cool slightly.
03 - In a small saucepan, combine blackberries, sugar, and lemon juice. Cook over medium heat until berries break down and mixture thickens, about 8-10 minutes, stirring frequently. Puree with a hand blender, then strain through a fine mesh sieve to remove seeds. Let cool completely.
04 - Using an electric mixer, beat cream cheese and sugar until smooth and creamy. Add eggs one at a time, mixing well after each addition. Blend in sour cream, vanilla extract, and flour until just combined. Do not overmix.
05 - Pour cheesecake filling over the cooled crust. Dollop spoonfuls of blackberry puree over the top, then swirl gently with a skewer or knife to create a marbled effect.
06 - Place springform pan in a larger baking tray and fill with hot water to create a water bath. Bake for 50-60 minutes until center is almost set but slightly wobbly.
07 - Turn off oven, crack door open, and let cheesecake cool slowly for 1 hour. Remove from oven and refrigerate for at least 4 hours or overnight before serving.
08 - Before serving, garnish with fresh blackberries, mint leaves, and whipped cream if desired. Run a warm knife around the edge before releasing the springform ring.