Put the flour in a food processor. Add the butter and process until the mixture resembles coarse breadcrumbs. Add the confectioner's sugar and vanilla and process until the mixture comes together to form a dough. Knead lightly and shape into a thick sausage. Wrap and chill for at least 1 hour until firm.
Preheat the oven to 400. Grease two baking sheets. Using a sharp knife, cut 1/4 inch thick slices from the dough and space them slightly apart on the baking sheet.
Bake for 8-10 minutes, alternating the position of the baking sheets in the oven halfway through cooking, if necessary,until the biscuits are cooked evenly and have just turned pale golden around the edges. Leave for 5 minutes, then transfer to a wire rack to cool. Serve dusted with confectioner's sugar.