Whisk the flour and cornstarch in a medium bowl to blend.
Using an electric mixer, beat the butter and ½ of cup powdered sugar in a large bowl until light and fluffy.
Mix in the lime juice, lime peel, and lime oil.
Beat in the flour mixture until it is smooth.
Refrigerate the dough until just firm, about 45 minutes.
Using a scant tablespoon for each, form the dough into balls and place them on prepared sheets, spacing them one inch apart.
Bake the cookies until they're pale golden on top and browned on bottom, about 23 minutes.
Transfer the baking sheets to cooling racks; immediately sift a generous amount of powdered sugar over the cookies.
Cool the cookies completely on the baking sheets.
May 31, 2008 Excellent: sort of a cross between a Butterball and a Melting Moment Cookie. Very lime-y. Tossed them in a bag with powdered sugar to coat. It made a small batch: one and a half pans. (I found lime oil at the River Valley Co-op in Northampton)