Preheat the oven to 350F degrees and line 2 cookie sheets with parchment paper.
In a large bowl beat together the butter and sugar until fluffy.
In a separate bowl - sift together the cornstarch and flour.
Beat the flour mixture into the butter mixture about 1/2 at a time until all the flour is incorporated. If the dough feels sticky, cover the bowl with plastic wrap and refrigerate for 30 minutes.
Form the dough into balls about 2 teaspoons in size (about the size of a ping pong ball) and place 2 inches apart on the lined cookie sheet.
Bake 1 sheet at a time for 12-15 minutes or until the tops look set.
Remove from the oven and cool completely.
Place the chopped chocolate in a large, heat-proof bowl.
Microwave on medium power for 45 -second intervals, stirring between each interval until melted. Stir in the vegetable oil.
Dip 1/2 of each cookie in the melted chocolate (or simply spread the chocolate on half of each cookie with a knife or the back of a spoon, and optionally add a few sprinkles on top of each cookie.