Filling

1. Purée 1 cup blackberries in a blender or food processor and strain. Discard seeds. You should have about 1/3 cup purée. Stir in blackberry liqueur and 2 teaspoons sugar. Set aside until ready to use.
2. Mix cream cheese and remaining 1 cup sugar in bowl of an electric mixer on low speed until blended. Add vanilla. Add eggs, 1 at a time, on low speed. Add sour cream and mix until blended. Spoon half batter into cooled crust. Drop half blackberry purée mixture into batter, 1 teaspoon at a time. Swirl into filling using a toothpick or wooden skewer. Repeat with remaining batter and blackberry purée mixture. Bake about 50 minutes or until edges are just set and center jiggles slightly. Turn oven off and prop the door ajar with the handle of a wooden spoon. Let cool in oven for 1 hour. Remove from oven and cool completely. Place in refrigerator and chill until cold throughout, 4 to 6 hours or overnight.
3. To serve, make a pile of remaining blackberries on top of cheesecake and garnish with mint leaves.

Crust

1. Preheat oven to 350°F. Combine chocolate wafer crumbs and melted butter in a medium bowl. Press into and up sides of 9-inch non-stick springform pan (if pan is not nonstick, brush first with melted butter). Bake about 14 minutes or until firm. Let cool completely. Reduce oven temperature to 300°F.