Preheat the oven to 350°F (175°C). Grease a 9×9 inch pan.
Combine graham cracker crumbs, ⅓ cup sugar, and melted butter in a mixing bowl. Press the mixture firmly into the bottom of the prepared pan to form a crust.
Beat the softened cream cheese in another bowl until smooth.
Gradually add 1 cup sugar and vanilla extract, and beat until well combined.
Add the eggs, one at a time, mixing well after each addition.
Pour the cream cheese mixture over the graham cracker crust in the pan.
Drop spoonfuls of raspberry puree on top of the cheesecake mixture and swirl gently with a knife to create a marbled effect.
Bake for 30-35 minutes or until set.
Remove from the oven and let cool to room temperature. Chill in the fridge for at least 2 hours before serving.
Cut into bars and garnish with fresh raspberries if desired.
