In a bowl, with a mixer on medium speed, beat butter, granulated sugar, and vanilla until smooth. Add flour and salt and mix on low speed until dough comes together in a ball. Transfer to a lightly floured surface.
Divide dough in half. With a lightly floured rolling pin, roll each portion to about 1/8 inch thick. With a floured 2- to 3-inch round or star-shaped cutter, cut out cookies. If desired, cut a 1/2-inch circle out of the center of half of the cookies to make a window for the jam filling (see notes). Place cookies 1 inch apart on buttered 12- by 15-inch baking sheets. Gather excess dough into a ball, reroll, and cut out remaining cookies.
Bake in a 325° regular or 300° convection oven until edges are just beginning to brown, 10 to 12 minutes. If baking more than one sheet at a time in one oven, switch positions halfway through baking. Transfer cookies to racks to cool completely.
Spread the flat side of each of half the cookies (those without holes) with about 1/2 tablespoon jam. Top each with a remaining cookie (with a hole), flat side toward filling. Sprinkle tops of cookies evenly with powdered sugar.
Nutritional analysis per sandwich cookie.