01 - Preheat the 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 the 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 the berries break down and the mixture thickens (about 8-10 minutes), stirring frequently. Puree with a hand blender and then strain through a fine mesh sieve to remove seeds. Let cool.
04 - Using a 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.
05 - Pour the cheesecake filling over the cooled crust. Dollop spoonfuls of the blackberry puree over the top, then swirl gently with a skewer or knife for a marbled effect.
06 - Bake in a water bath (place the pan in a larger tray filled with hot water) for 50-60 minutes, until the center is almost set but slightly wobbly.
07 - Turn off the oven, crack the door open, and let the cheesecake cool slowly for 1 hour. Remove from the 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.