Preheat your oven to 325°F (160°C) and prepare a 9x13-inch baking pan by lining it with parchment paper, leaving some overhang for easy removal and greasing it lightly.

In a mixing bowl, combine graham cracker crumbs and granulated sugar. Pour in melted unsalted butter, and mix until the mixture resembles wet sand.

Transfer the crumb mixture into the prepared pan, and press it firmly into an even layer. Bake for about 10 minutes, until golden brown, then allow to cool.

Using an electric mixer, beat the softened cream cheese until smooth. Gradually add in sour cream, eggs, and vanilla bean paste until combined.

Fold in the raspberry puree gently into the cream cheese mixture, aiming for a marbled effect.

Pour the raspberry-infused filling over the cooled crust, spreading it evenly, then scatter fresh raspberries on top, pressing them down slightly.

Bake for 30-35 minutes, until edges are set but the center jiggles slightly.

Turn off the oven and crack the door open, allowing the cheesecake to cool for about an hour.

After cooling, let the cheesecake bars reach room temperature, cover, and refrigerate for at least 4 hours or overnight.

When ready to serve, lift the bars out using the parchment paper, slice into squares, and enjoy them chilled.