Preheat the oven to 350°F, line two cookie sheets with silicone baking mats.
Use a stand mixer with the paddle attachment, beat the butter, oil, sugar, and confectioners sugar until combined.
Beat in the egg, cotton candy extract, and heavy whipping cream until combined
Mix dry ingredients; in a medium size mixing bowl, whisk together the flour, corn starch, salt, and baking powder.
Gradually beat the dry ingredients into the wet and continue beating until a dough forms.
Using a medium cookie scoop and food scale (optional)scoop out a small amount of dough and weigh it. You want your dough to be 2.2oz or close to make 12 equal size cookies.
Roll the cookie dough into a ball and place it on the cookie sheet, pressing into a thick disk.
Repeat steps until you have 6 even-size cookie dough disks on your cookie trays Bake in the oven for 10 minutes.
Allow the cookies to cool completely on a wire cooling wrack while you make the frosting.