Sift the flour,
cornstarch, baking powder, and salt into a large
bowl. Use a pastry blender to cut in the butter
until the mixture resembles fine crumbs.
Mix in
the sugar, eggs, and vanilla to form a smooth dough. Wrap in plastic wrap and refrigerate for 30
minutes.
Preheat the oven to 375°F/190°C/gas 5. Set out two cookie sheets. Roll out the
dough on a lightly floured surface to a thickness of
1/4 inch (5 mm).
Use a 2-inch (5-cm) cookie cutter
to cut out the cookies. Gather the dough scraps,
re-roll, and continue cutting out cookies until all
the dough is used.
Use a spatula to transfer the
cookies to the cookie sheets, placing them 1 inch
(2.5 cm) apart. Prick the cookies all over with a
fork.
Bake, one sheet at a time, for 10-15
minutes, or until just golden at the edges. Transfer to racks and let cool completely.