Preheat the oven to 325°F (160°C). Grease the baking dish or line it with parchment paper for easy removal.
In a mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Mix until well combined. Press this mixture firmly into the bottom of the prepared baking dish. Bake for 10 minutes, then remove from the oven and let it cool.
In another mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth and creamy. Add the granulated sugar and continue to mix until well combined.
Add the vanilla extract and mix again. Incorporate the eggs one at a time, mixing well after each addition. Then, fold in the sour cream until smooth.
Gently fold in the fresh raspberries, taking care not to break them up too much.
Pour the cheesecake filling over the cooled crust, spreading it evenly.
Bake in the preheated oven for 35-40 minutes, or until the edges are set but the center still has a slight jiggle.
Once baked, turn off the oven, crack the door open, and allow the cheesecake to cool in the oven for about 1 hour.
Once cooled, refrigerate the cheesecake bars for at least 4 hours, preferably overnight, before slicing into bars.
Cut into 12 equal pieces and serve chilled.