Cream the butter and confectioners’ sugar together until light.
Sift the flour and salt together and add to the creamed mixture. Add the vanilla and blend thoroughly.
Gather the dough into a ball, wrap in wax paper, and chill for 4 to 6 hours.
Roll out the chilled dough to ⅝-inch thickness. Using a 3-inch-long heart-shaped cookie cutter, cut out cookies. Sprinkle the tops with granulated sugar. Place the cut-out cookies on ungreased cookie sheets and refrigerate for 45 minutes before baking.
Preheat the oven to 325°F.
Bake until just starting to color lightly, 20 minutes; the cookies should not brown at all. Cool on a rack.