In a small bowl combine sugar and orange zest. Using the back of a spoon crush the sugar and zest together.
In a saucepan combine 1 1/2 cups blackberries, 3 TBSP of orange sugar and the orange juice.
Cook and stir over medium high heat until berries are soft. (About 5 minutes).
Press mixture through a fine mesh sieve and discard seeds. Set aside.
Stir together shortbread crumbs, butter, and ginger until well combined. Press into the bottom of a 9 inch springform pan. Bake 10 minutes and set aside to cool.
Beat cream cheese, 1 cup orange sugar, flour, lemon zest, and vanilla with electric mixer on medium speed until combined.
Add eggs one at a time, beating on low speed after each addition until just combined.
Remove 1 1/2 cups of batter and transfer to a separate bowl. Add the blackberry syrup to batter.
Pour half of remaining batter into crust. Pour half of the blackberry batter over the plain. Carefully spoon remaining plain batter over blackberry batter. Top with remaining blackberry batter. Using a knife swirl blackberry batter into plain batter.
Bake 50-60 minutes or until a 2 1/2 inch area around sides appears set.
Cool on wire rack for 15 minutes. Loosen around edges. Cool 20 more minutes and remove sides of pan. Cool completely.
Cover and chill overnight.
Stir remaining blackberries with remaining orange sugar. Cover and chill overnight. Stir before using.