Preheat your oven to 350°F (175°C).

In a mixing bowl, combine graham cracker crumbs with melted butter until they resemble wet sand. Press this mixture into the bottom of a springform pan and bake for about 8-10 minutes.

In a large mixing bowl, beat the cream cheese and sugar together until smooth. Add eggs one at a time, mixing well. Finally, blend in the vanilla extract and cocoa powder.

In a separate bowl, mix strawberry puree, additional sugar, and lemon juice until smooth.

Pour half of the chocolate filling into the crust, dollop strawberry mixture on top, then pour remaining chocolate filling. Swirl with a toothpick.

Bake for 50-60 minutes, until edges are set and center has a slight jiggle.

Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour to cool gradually.

Allow the cheesecake to cool to room temperature, then refrigerate for at least 4 hours or overnight.

Remove from the springform pan and garnish with fresh strawberries or whipped cream if desired.