Preheat the oven to 350 degree F. with a rack in the middle. Lightly butter a cookie sheet.
In a medium bowl, cream together the butter and sugar. Add the cornstarch and beat until smooth.
Slowly mix in the flour until combined, but crumbly. With your hands, form the dough into a ball.
Turn the dough out onto a lightly floured surface and pat the dough out to about 1⁄2-inch thick. Cut the cookies out with a 2 1⁄4-inch cutter (we use a tomato paste can).
Place the cookies on the sheet and bake for about 12 to 15 minutes or until the bottoms turn a very light golden brown, be sure not to over bake. Immediately transfer the cookies to a wire rack to cool to room temperature.
Meanwhile, fill a small saucepan halfway with water and bring to a boil over high heat. Place a glass bowl (or heat safe bowl) over the saucepan. Break the chocolate into pieces and place in the top bowl. Stir occasionally as the chocolate begins to melt until smooth.
When the cookies have cooled dip them halfway in the chocolate and place on waxed paper. Allow the chocolate to set up before serving.
