Line a 9-by-13-inch baking pan with parchment paper, allowing a couple of inches of overhang on the longer sides. Spray with nonstick cooking spray.

Place the graham crackers in a zip-top bag and use a rolling pin to crush into fine crumbs (about 3 cups). Transfer to a large bowl along with the granulated sugar and melted butter. Mix well and add to the bottom of the lined pan. Press the mixture firmly and evenly into the bottom of the pan, then set aside.

In a blender, combine the cream cheese, yogurt, powdered sugar, and vanilla, then blend until smooth. Transfer to a large bowl. Fold in the whipped topping. Pour the mixture over the top of the prepared crust and smooth it out.

Add spoonfuls of the raspberry preserves to the top and, using a skewer or knife, swirl the preserves. Arrange the raspberries in a grid across the pan. Cover and refrigerate until completely chilled and firm, about 3 hours.

Using the parchment sling, carefully lift out the cheesecake and transfer it to a cutting board. Slice the cheesecake into 16 or 20 squares, each topped with a raspberry.