Preheat oven to 350°F. Line a 9×9-inch baking dish with parchment paper, leaving some overhang on the sides for easy removal.
In a medium bowl, combine the graham cracker crumbs, butter, and sugar. Mix until the mixture resembles wet sand. Press the crust firmly into the bottom of the prepared baking dish.
In a large bowl, use a hand mixer to beat the cream cheese, eggs, sugar, vanilla, and salt until smooth. Spread the cream cheese mixture evenly over the prepared crust.
Scatter the fresh raspberries evenly over the cream cheese layer. If the raspberries are particularly large, cut them in half for more even distribution. Gently press them into the cream cheese to help them settle slightly.
In a medium bowl, whisk together the all-purpose flour, light brown sugar, and kosher salt. Stir in the melted butter until the mixture forms a crumbly dough.
Sprinkle the crumble topping evenly over the raspberries.
Bake the bars for 35-40 minutes, or until the center is set and the crumble topping is lightly golden.
Transfer the baking dish to a wire rack and let the bars cool completely at room temperature, about 1 hour.
Once cooled, transfer the dish to the refrigerator to chill for at least 1 hour before slicing and serving.