Cream butter, sugar, and vanilla with a mixer. Beat in flour and salt until just combined. Wrap in plastic; refrigerate until firm, at least 2 hours or overnight.
Roll out dough on a lightly floured surface to 1/8 inch thick. Cut out with a 1 3/4-inch scalloped round cutter, and transfer to a parchment-lined baking sheet; place in the freezer to harden for 30 minutes. Cut out letter or heart shapes from half the cookies, then return to freezer for another 15 minutes.
Heat oven to 325 degrees. Bake until cookies just begin to brown around the edges, 12 to 14 minutes. Cookies will keep airtight at room temperature about 5 days.
Shortly before serving, spread scant 1 teaspoon jam on whole cookies; gently top with cut-out cookies. Refrigerate until ready to serve, up to 3 hours. Finished cookies can sit at room temperature up to 3 hours.