01 - Preheat the oven to 325°F (160°C). Line a 9×9-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal.
02 - In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter, stirring until the mixture resembles wet sand. Press firmly and evenly into the bottom of the prepared pan. Bake for 8 minutes, then set aside to cool slightly.
03 - Combine the chopped strawberries, sugar, and lemon juice in a small saucepan over medium heat. Cook for 5–7 minutes, stirring frequently and mashing the berries with a spoon, until the mixture thickens into a syrupy reduction. Blend with an immersion blender or standard blender until smooth. Set aside to cool.
04 - In a large bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Add the sugar and beat until fully incorporated. Add the eggs one at a time, mixing well after each addition. Blend in the vanilla extract, sour cream, and flour until just combined — do not overmix.
05 - Pour the cheesecake batter over the baked crust and spread into an even layer. Drop spoonfuls of the cooled strawberry puree across the surface. Using a knife or skewer, gently drag through the batter in a figure-eight motion to create a marbled swirl pattern.
06 - Bake for 30–35 minutes, until the edges are set and the center has a slight jiggle. Avoid overbaking — the bars will continue to set as they cool.
07 - Remove from the oven and allow to cool to room temperature. Refrigerate for at least 2 hours until fully chilled and firm. Lift the bars out of the pan using the parchment paper overhang and cut into 16 even squares.