Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper or foil, leaving enough overhang to lift the bars from the pan.
Crush the graham crackers into fine crumbs using a food processor.
In a medium bowl, combine the graham cracker crumbs, brown sugar, melted butter, and salt. Press the mixture firmly and evenly into the bottom of the prepared pan.
In a large bowl, beat the softened cream cheese, granulated sugar, and flour with a hand mixer or stand mixer until smooth and creamy.
Reduce the mixer speed to medium. Add the eggs one at a time, mixing just until combined after each addition.
Add the sour cream, vanilla extract, lemon juice, and salt. Mix until smooth, being careful not to overmix.
Spread the cheesecake filling evenly over the crust.
Drop spoonfuls of raspberry preserves over the filling. Use a knife or skewer to gently swirl the preserves into the cheesecake batter.
Bake uncovered for 35–40 minutes, or until the edges are set and the center is slightly jiggly.
Let the cheesecake bars cool completely at room temperature.
Cover and refrigerate for at least 4 hours, or preferably overnight, until fully chilled and set.
Lift the cheesecake from the pan, cut into 12 bars, and serve.
Notes
Use room-temperature cream cheese, eggs, and sour cream for a smoother cheesecake filling.Avoid overmixing the batter after adding the eggs, as this can incorporate excess air and cause the cheesecake to crack.For clean slices, chill the cheesecake bars thoroughly and wipe the knife clean between cuts.Store leftovers covered in the refrigerator.