In a small bowl, combine the graham cracker crumbs and the melted butter until the crumbs are completely moistened.
Press the crumb mixture into the bottom of a 9-inch springform pan and up the sides just slightly, to form a crust. Chill to set.
Melt the white chocolate in the microwave (break it into small pieces first) on 50% power for 30-second increments until the chocolate is just melted. Set it aside to cool slightly to just above room temperature.
Beat the cream cheese on medium speed until very smooth. The cream cheese MUST be at room temperature.
Sift the powdered sugar, add it on top of the cream cheese and beat well until incorporated.
By this point the melted chocolate should be close to room temperature. Your cream cheese mixture MUST be at room temperature or it will cause the chocolate to solidify during the mixing process, creating chocolate chunks in the cheesecake batter (the cheesecake will lose its silky smooth texture).
Beat on medium speed until the chocolate is fully incorporated (scrape down the sides of the bowl well here).
Fold in the whipped cream or whipped topping gently until fully incorporated.
Add half the cheesecake filling into the pan with the crust, then swirl half of the jam on top. Add the rest of the cheesecake filling, smoothing out the top, then dollop the rest of the jam on top and create a swirl pattern with a knife or wooden skewer.
Chill the cheesecake in the fridge overnight (OR for 4-6 hours plus 1 hour in the freezer) before slicing and serving.
Serve with a dollop of whipped cream and fresh blueberries, if desired.