My friend Jan Swain makes and shares these melt-in-your-mouth cookies every Christmas. They’re the best gift I can imagine.
In a mixer on low speed, cream together butter and sugar until fluffy. Add flour and vanilla extract and mix just until a soft dough forms. Turn onto a floured surface and divide into three equal balls. Flatten balls and shape into flattened disks, about 7 inches wide and ½ inch thick.
Prick the disks all over with a fork; place on oiled baking sheets, wrap in plastic, and refrigerate, covered, at least 2 hours or overnight.
Preheat oven to 375°. Bake 5 minutes, then reduce heat to 300° and bake, rotating sheets occasionally, until slightly firm to the touch and barely golden at the edges, 45 to 60 minutes. Remove from oven and cool slightly, 5 to 10 minutes. With a large sharp knife, cut each disk in half and then into 16 thin diagonal wedges (handle gently; they crumble easily). Dust with additional confectioners’ sugar. Cookies will keep fresh up to 2 weeks in an airtight container, and will also freeze well.