Using an electric beater, cream the butter and sugar in a large bowl. Add the egg and vanilla extract and mix well. In another bowl, combine the flour, baking powder, and salt. Mix in the flour a little at a time until the ingredients are well combined. Chill the dough for several hours or overnight.
Heat the oven to 350 degrees. Divide the dough into 3 parts. Working on a floured surface with one part at a time, roll out the dough to a 1/4-inch thickness. Using a knife, cut out corncob shapes about 4 inches long. Place the cookies on ungreased baking sheets and bake for 9 minutes or just until the edges brown. Let the cookies set on the sheets for about 2 minutes, then transfer them to a wire rack to cool completely.
Frost the cooled cookies. Next, use kitchen shears to cut husks from the fruit leather to fit the sides of each cookie. Press the husks in place atop the frosting, with the tips down a bit. Now fill in the middle with candy kernels gently pressed into place. Makes about 1 1/2 dozen cookies.