Preheat your oven to 325°F (160°C) and line an 8x8-inch baking pan with parchment paper, leaving some overhang for easy removal later.
In a medium bowl, mix the graham cracker crumbs, ⅓ cup sugar, and melted butter until well combined. Press the mixture firmly into the bottom of the prepared pan to form the crust. Bake for 10 minutes, then remove and let cool slightly.
In a large mixing bowl, beat the softened cream cheese with 1 cup of granulated sugar until smooth and creamy.
Add the eggs, one at a time, mixing well after each addition. Then add the sour cream, lemon juice, and lemon zest, and mix until fully combined.
In a separate small bowl, mix the pureed strawberries with 1 tablespoon of cornstarch until smooth. This will help keep the strawberry layer from getting too runny.
Divide the cheesecake batter in half, and mix the pureed strawberry mixture into one half of the batter until well blended.
Pour the plain cheesecake batter into the cooled crust first, spreading it evenly. Then gently spoon the strawberry cheesecake batter over the top, allowing it to create a marbling effect as desired.
Using a toothpick or knife, swirl the strawberry batter into the plain batter for a marbled design.
Bake for 30-35 minutes or until the cheesecake is set but still slightly jiggly in the center.
Once baked, allow it to cool at room temperature, then refrigerate for a minimum of 4 hours, or overnight for best results.
When ready to serve, lift the cheesecake bars out of the pan using the parchment overhang, slice into squares, and garnish with fresh strawberry slices and a sprinkle of lemon zest if desired.
Notes
For best results, refrigerate overnight before serving.