In an electric mixer fitted with a paddle attachment, cream butter, sugar and vanilla until combined. On slow speed, beat in flour and salt until combined. Wrap dough in plastic wrap; chill until very firm, at least 2 hours or overnight.
On a lightly floured surface, roll out the dough until 1/8 inch thick. Cut out hearts,or the cutter of your choice, with a 2-inch cutter. Transfer cookies to an ungreased baking sheet. Chill for 30 minutes.
Heat oven to 300F with rack in center. Press the tines of a fork into each cookie to make designs. Bake until just beginning to brown around the edges, about 19 minutes. Cookies will keep in an airtight container for about 5 days.
Melt the chocolate in a heat-proof bowl, on the top of a double boiler, over 1-inch of simmering water, stirring occasionally. Stir in the oil. Dip half or one-third of each cookie into the chocolate mixture. Transfer cookies to a cooling rack to dry, or place them on parchment paper in the freezer for 10 minutes.