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Add the flour and salt and buzz again until combined. Add the butter and process until the mixture start to look sort of pebbly, like coarse crumbs. Then you can add the egg and vanilla. Keep processing until the dough comes together.
Lightly dust a clean surface with the remaining flour and turn out the dough on top. Form the dough into a ball and then flatten it into a disk, working in some of the flour from the table, as needed. Wrap in plastic wrap and place in the freezer for about 30 minutes or in the refrigerator for about 1 hour. The dough should be slightly firm so you can roll it with a rolling pin.
Roll about 1/4-inch thick, sprinkling the surface and the rolling pin with flour if it starts to stick. Cut out cookies from the chilled dough with a 2-inch cookie cutter. Space them about an inch apart on parchment-paper-lined baking sheets.
Place one of the beautiful toasted pecan halves in the center of each cookie and dust with a light sprinkling of sugar. Bake 18 to 20 minutes, or until the cookies are a lovely sandy color, rotating the sheets halfway through baking. Cool the cookies completely before storing them in airtight containers of vintage tins.