Preheat your oven to 325°F (163°C) and line the baking dish with parchment paper, leaving some overhang for easy removal later.

In a mixing bowl, combine the graham cracker crumbs, melted butter, and 2 tablespoons of sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared baking dish to form the crust.

In another bowl, beat the softened cream cheese until smooth. Gradually add the 1 cup of sugar, beating until well incorporated.

Add the eggs, one at a time, mixing well after each addition. Then, stir in the vanilla extract and sour cream until smooth and creamy.

Pour the cheesecake mixture over the crust, spreading it evenly.

In a small saucepan, combine the raspberries, ¼ cup sugar, cornstarch, and lemon juice. Cook over medium heat until the raspberries break down and the mixture starts to thicken, about 5-7 minutes. Remove from heat and let cool slightly.

Spoon the raspberry mixture over the cheesecake layer. Use a knife to gently swirl the raspberry layer into the cheesecake, creating a marbled effect.

Bake in the preheated oven for 35-40 minutes, or until the cheesecake is set and the edges are slightly golden.

Allow the cheesecake bars to cool at room temperature for an hour. Then, refrigerate for at least 3 hours (or overnight) to fully set.

Once set, lift the bars out of the pan using the parchment paper overhang. Cut into square bars and serve.