Preheat oven to 350 degrees.Mix the butter and sugar together in a large bowl until just combined. Stir in vanilla. Add the flour and salt and mix until dough comes together. Form a small ball of dough in your hands and pinch between two fingers. Dough should be soft and pillowy, and should not crack when pinched. If cracks form, return to bowl and add 1-2 tablespoons of water. Repeat as needed. Turn onto a piece of plastic wrap and top with another piece of plastic wrap - no need to flour the plastic. Roll dough 1/4-inch thick between the two pieces of plastic wrap. Wrap tightly and transfer sheet of dough to the freezer for 15 minutes, or the fridge for up to 3 days. Gently unwrap chilled dough and cut with a 2- to 3-inch round or fluted cutter. Place rounds on baking sheets lined with parchment paper. Cut out the center of half the rounds using a 1-inch cutter. Bake 12-14 minutes, until cookies are set and just begin to brown. Do not overbake! Cool to room temperature.To assemble: Sift powdered sugar over the cookies with the centers cut out (these will be the tops). Spread filling on the flat sides of the uncut cookies (these will be the bottoms). Gently press the flat sides together of one top and one bottom cookie to form a sandwich. Store assembled cookies in an airtight container in the fridge for up to 5 days.
For the filling: Any fruit preserves (strawberry, raspberry, blackberry, apricot, etc.), melted chocolate (dark, semi-sweet, or white), or lemon curd are all good options here. Keep in mind what color you want the filling to be.To freeze and make later: Bake cookies according to recipe directions, but do not assemble! Freeze baked shortbread in an airtight container. Remove from freezer when ready to assemble. Shortbread will keep in the freezer for up to 3 months.