Prepare the Crust: Preheat oven to 350°F (175°C). Grease and line a 9×13 inch baking pan with parchment paper, leaving an overhang for easy removal. In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Press evenly into the bottom of the prepared pan. Bake for 8-10 minutes until lightly golden. Let cool.

Make the Strawberry Compote: While the crust cools, prepare the strawberry topping. In a saucepan, combine the chopped strawberries and sugar. Cook over medium heat, stirring occasionally, until the strawberries break down and release their juices. In a small bowl, whisk together water and cornstarch. Stir the cornstarch mixture and lemon juice into the strawberry mixture. Cook, stirring constantly, until the compote thickens. Remove from heat and let cool slightly.

Make the Cheesecake Filling: In a large bowl, beat the softened cream cheese and sugar together until smooth and creamy. Beat in the sour cream and vanilla extract until well combined. Beat in the eggs one at a time, mixing until just incorporated. Be careful not to overmix.

Assemble and Bake: Pour the cheesecake filling over the cooled crust. Spread evenly. Spoon the slightly cooled strawberry compote over the cheesecake filling. Use a knife or skewer to gently swirl the strawberry through the cheesecake batter.

Bake: Bake for 25-35 minutes, or until the edges of the cheesecake are set and the center is just slightly jiggly.

Cool and Chill: Let the cheesecake bars cool completely at room temperature for about 1-2 hours. Then, cover and refrigerate for at least 4 hours, or preferably overnight, to allow them to fully set.

Serve: Lift the cheesecake bars out of the pan using the parchment paper overhang. Cut into squares and garnish with fresh strawberry slices or a drizzle of melted white chocolate, if desired.