Prepare the Crust: Mix graham cracker crumbs, melted butter, and sugar together in a bowl. Press the mixture into the bottom of a springform pan to form an even crust. Refrigerate for 10 minutes to set.
Make the Cheesecake Filling: Beat the cream cheese, heavy cream, powdered sugar, and vanilla extract together in a mixing bowl until smooth and thick.
Prepare the Strawberry and Chocolate Swirls: Divide the cheesecake mixture into two parts. Mix the strawberry puree into one half, and the melted chocolate, cocoa powder, and sugar into the other half.
Assemble the Cheesecake: Spoon alternating spoonfuls of the strawberry and chocolate cheesecake mixtures onto the crust. Use a toothpick or knife to swirl the two mixtures together to create a marbled effect.
Chill: Refrigerate the cheesecake for at least 4 hours, or overnight, to let it set.
Serve: Remove from the pan, slice, and serve chilled. Garnish with extra strawberries or chocolate shavings if desired.