Preheat your oven to 325°F (163°C). Line a 9x9-inch square baking pan with parchment paper, leaving an overhang for easy removal.
Make the Crust:
In a medium bowl, mix together the graham cracker crumbs, granulated sugar, and melted butter until evenly combined. Press the mixture firmly into the bottom of the prepared pan. Bake for 10 minutes, then set aside to cool slightly.
Prepare the Raspberry Swirl:
In a small bowl, stir together the raspberry preserves and water until smooth. Set aside.
Make the Cheesecake Filling:
In a large mixing bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the eggs one at a time, mixing well after each addition. Beat in the vanilla extract, sour cream, and flour until fully incorporated.
Assemble the Bars:
Pour the cheesecake filling over the cooled crust, spreading it evenly. Drop small spoonfuls of the raspberry mixture on top of the filling, then use a toothpick or knife to swirl the raspberry mixture gently into the cheesecake.
Bake:
Bake in the preheated oven for 40-45 minutes, or until the edges are set and the center is slightly jiggly. Avoid overbaking as the cheesecake will firm up as it cools.
Cool and Chill:
Allow the cheesecake bars to cool to room temperature, then refrigerate for at least 2 hours, or until fully chilled.
Slice and Serve:
Use the parchment paper overhang to lift the bars out of the pan. Slice into 16 squares and serve chilled.