01 - Preheat oven to 325°F. Line a 9x9-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal.
02 - In a medium bowl, combine graham cracker crumbs, sugar, and melted butter 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.
03 - Combine chopped strawberries, sugar, and lemon juice in a small saucepan over medium heat. Cook for 5–7 minutes, stirring and mashing the berries until the mixture reduces into a thick, syrupy consistency. Blend until smooth using an immersion blender or standard blender, then set aside to cool.
04 - In a large bowl, beat the cream cheese with an electric mixer until smooth and creamy. Add sugar and beat until fully incorporated. Add eggs one at a time, mixing well after each addition. Blend in vanilla extract, sour cream, and flour until just combined — do not overmix.
05 - Pour the cheesecake batter over the cooled crust and spread into an even layer. Drop spoonfuls of the cooled strawberry puree across the surface, then gently drag a knife or skewer through the puree in figure-eight motions 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 firm up as they cool.
07 - Cool the pan to room temperature, then refrigerate for at least 2 hours. Lift the bars out using the parchment paper overhang and cut into 16 even squares. Serve chilled.