Put 1/2 cup each of the blackberries and blueberries in a saucepan and add the sugar, blackberry jam, honey, lemon zest, vanilla extract and 1/4 cup water. Bring to a boil and simmer for 5 minutes. Using a potato masher, mash the berries gently until they are good and broken up.
Add the remaining 2 cups each blackberries and blueberries to a mixing bowl. Pour the warm berry mixture over the fresh berries and fold everything together with a spatula until well coated. Allow everything to cool 10 minutes or so before serving. Serve atop your favorite dessert.