Preheat oven to 350 degrees F. Grease a mini muffin tin well with nonstick cooking spray.
Combine the powdered sugar, flour, and 3/4 cup butter in a food processor. If necessary, add 2-3 tbsp more of butter 1 tbsp at a time until a firm dough forms (you don't want it to be crumbly, but it shouldn't be sticky either).
Scoop dough by the tablespoon and press into the mini muffin tin.
Bake for 10 minutes. Press the back of a tablespoon into each crust IMMEDIATELY upon removing from the oven. This creates the indentation for the filling. Let cool completely.
Meanwhile, beat together the cream cheese, granulated (yes! granulated.) sugar, and the vanilla until smooth. Spoon the cream cheese filling into a ziptop bag.
Once the crusts have cooled and been removed from the pan (I do this by gently pressing down on the edges and twisting, and they come out pretty easily; but you could also tap the bottom of the pan to release more than one at a time), snip the corner of the filling bag and pipe about a tablespoon of filling into each crust.
In a small bowl, whisk together the lime juice and the corn syrup. Top each tartlette with a couple of raspberries, and brush the lime glaze over top. If possible, chill before serving.
The crusts can be filled and chilled ahead of time, but do not top with fruit or glaze until just before serving. Otherwise the juices will "bleed" into the filling. Store covered in the refrigerator.