The vanilla shortbread cookie recipe from Epicurious and the lemon meltaway cookie recipe from MyRecipes are examples of cookie recipes that include cornstarch as an ingredient. Both recipes are highly rated and easy to follow.
To make the vanilla shortbread, cream 2 sticks of softened unsalted European-style butter in a bowl until the butter is light and fluffy. Slowly beat in 1/4 cup of granulated sugar and 1 teaspoon of vanilla extract. Combine 2 cups of all-purpose flour, 3/4 cup of confectioners' sugar, 1/4 cup of cornstarch and 1/4 teaspoon of salt in another bowl. Gradually add the flour mixture to the butter mixture to form dough.
Divide the dough into two 6-inch-long logs, wrap the logs in plastic, and chill them in the refrigerator for at least two hours. Slice each log into 1/3-inch-thick pieces, and place the pieces on baking sheets. Bake the vanilla shortbread at 325 F for approximately 18 minutes or until the cookies turn a light golden color.
To make the lemon meltaways, cream 1 3/4 sticks of softened butter before beating in 1/2 cup of confectioners' sugar. Fold in 2 tablespoons of lemon juice and 1 tablespoon of lemon zest. Combine 1 1/2 cups of all-purpose flour, 1/4 cup of cornstarch and 1/4 teaspoon of salt in another bowl. Gradually incorporate the flour mixture into the butter mixture to make dough.
Chill the dough in the refrigerator for one hour before placing 1-inch dollops of the dough on lined baking sheets. Bake the lemon meltaways at 350 F for 13 minutes or until they start to brown at the edges, and let them cool for five minutes before coating them with confectioners' sugar.