Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan with cooking spray or butter.

In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.

In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add 1 cup sugar and vanilla extract, mixing until well combined.

Add the eggs one at a time, mixing on low speed after each addition until just combined. Be careful not to overmix.

Stir in the sour cream until smooth. Divide the batter in half into two separate bowls.

In one bowl, sift in the cocoa powder and mix until fully incorporated. In the other bowl, add the pureed strawberries and 1/4 cup sugar, mixing until smooth.

Pour half of the chocolate batter into the prepared crust. Then, spoon half of the strawberry batter over the chocolate layer. Use a knife or skewer to swirl the two batters together gently. Repeat with the remaining batters.

Bake in the preheated oven for 55-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and crack the door open, allowing the cheesecake to cool in the oven for 1 hour.

Remove the cheesecake from the oven and let it cool to room temperature. Cover and refrigerate for at least 4 hours, preferably overnight, before serving.