First Step: Prepare the Raspberry Sauce
Start by mixing 1 teaspoon of water with the cornstarch in a small bowl until dissolved. In a saucepan over medium heat, combine your fresh or frozen raspberries (unthawed), 2 tablespoons of granulated sugar, optional lemon juice to brighten flavor, and the remaining 1 teaspoon water. Stir regularly while breaking up the berries. Once the mixture begins simmering, add the cornstarch mixture and continue cooking for about 3 minutes until thickened. Remove from heat and press the sauce through a fine mesh sieve to remove seeds. Allow it to cool completely, then chill for at least 30 minutes to enhance its texture.

Second Step: Preheat Oven and Prepare Pan
Preheat your oven to 350°F (177°C). Line a 9-inch square baking pan with parchment paper, leaving an overhang on two opposite sides to help lift the bars out easily after baking. This step simplifies cleanup and ensures neat removal.

Third Step: Make the Crust
If using Oreo cookies, pulse the cookies into fine crumbs (excluding the cream filling) and combine with 5 tablespoons of melted unsalted butter. For a graham cracker crust, mix graham cracker crumbs, melted butter, optional sugar, and a pinch of salt to balance. Press the combined crust mixture firmly and evenly into the bottom of the prepared pan. Bake for 8 minutes, then remove and let it cool completely on a wire rack to set.

Fourth Step: Melt the White Chocolate
Gently melt the white chocolate baking bars using a double boiler or microwave in short bursts, stirring frequently to achieve a smooth, homogeneous texture. Allow the melted chocolate to cool but remain liquid to incorporate smoothly into the cheesecake filling.

Fifth Step: Prepare the Cheesecake Filling
In a large mixing bowl, beat the softened cream cheese and 1/3 cup granulated sugar with an electric mixer on medium speed until smooth and glossy. Add the flour, lemon juice, vanilla extract, and salt; mix to combine well. Then add the eggs one at a time, mixing just until each is blended in. Avoid over-mixing to prevent incorporating too much air, which can cause cracks. Gently fold in the cooled melted white chocolate, trying to maintain a smooth consistency.

Sixth Step: Layer the Bars
Pour half of the cheesecake filling over the cooled crust, spreading evenly with a spatula. Drizzle half of the chilled raspberry sauce over this layer. Spread the remaining cheesecake filling atop the sauce layer. Finally, drizzle the remaining raspberry sauce on top and gently swirl with a toothpick or knife to create an attractive marbled effect.

Seventh Step: Bake the Cheesecake Bars
Bake in the preheated oven for 32 to 36 minutes at 350°F or 40 to 50 minutes at 325°F if using a water bath. The edges of the bars should be set and slightly golden with a tiny wobble in the center. If opting for a water bath for a silkier texture and crack prevention, remove the water bath pan and keep the oven door slightly open for an hour after baking to aid gradual cooling.

Final Step: Cooling, Chilling, and Serving
Allow the bars to cool at room temperature for about 45 minutes. Then place them in the refrigerator for at least 3 hours or overnight to fully set. Use the parchment paper overhang to lift the cheesecake bars from the pan, then cut into 16 squares using a sharp knife. Wipe the knife clean between cuts to maintain neat edges. Serve chilled for best flavor and texture. These bars pair wonderfully with fresh raspberries or a light dusting of powdered sugar.