Preheat oven to 375ºF. Prepare a 13x18 cookie sheet by spraying with baking spray.
In a stand mixer or a large bowl with hand beaters, beat the cold butter, oil, and sugars on low for 30 seconds. Scrape the bowl, then increase to medium speed for another 30 seconds, then high speed for 30 seconds, or until very light and fluffy.
18 tablespoons butter , ⅓ canola oil, 1 ½ cup granulated sugar, ¾ cup powdered sugar
Beat in the eggs one at a time, scraping after each one. Add the vanilla. Scrape well.
3 eggs, 2 teaspoons vanilla
In a medium bowl, combine the cornstarch, baking soda, salt, cake flour, and all-purpose flour. Add the flour mixture to the butter mixture and combine on low until just combined. The dough should be very moist. Scrape the bowl well.
1 ½ teaspoon cornstarch, 1 ½ teaspoon baking soda, ¾ teaspoon kosher salt, 2 ¼ cups cake flour, 3 cups all-purpose flour
Place dollops of dough around the sheet pan. Use clean hands or the back of a rubber spatula to press the dough evenly across the pan. Take your time because if it is uneven then the final product will be uneven.
Bake for 13-15 minutes. The edges should be very light golden brown and the center looks set. A toothpick will come out clean.
Once fully baked, remove from the oven and allow to cool completely.
Once the cookies have cooled, make the frosting by placing the butter, cream cheese, and powdered sugar into a stand mixer. Mix on low to combine then increase to medium speed until light and fluffy, about 3 minutes.
1 ½ cups butter, 3 ounces cream cheese, 6 ½ cups powdered sugar
Scrape the sides and bottom of the bowl. Add vanilla and 1 tablespoon of cream. Beat for 2 more minutes or until light and fluffy. Add additional cream if needed until the frosting is loose enough to spread, but still hold its shape.
3 teaspoon vanilla, 1-3 tablespoons heavy cream
Spread frosting over the top of the cooled cookies and decorate as desired.
Sprinkles