In an electric mixer with a paddle attachment, cream together butter, cream cheese, and both sugars. Add vanilla and egg.
Add flour, cornstarch, baking powder, baking soda, and salt. Mix until the dough pulls from the sides.
Use a 1.5 tablespoon cookie scoop to add mounds of dough to a parchment or silicone mat-lined baking sheet. Do not use nonstick cooking spray. This will cause the dough to spread.
Refrigerate for 1 hour. This step is necessary to keep the dough from spreading while it bakes.
Preheat the oven to 400℉. Place the baking sheet directly into the oven from the fridge.
Bake in the oven for 11-13 minutes, until the tops are lightly golden brown and the centers of the cookies are underdone. They will set as they cool.
Strawberry Buttercream Frosting
Crush freeze-dried strawberries into fine powder. A food processor or zip-lock bag and a rolling pin both work. Sift out any large pieces.
Whip butter on high speed in an electric mixer for 5 minutes. Add strawberry extract and strawberry powder.
Slowly add powdered sugar. Add 1-2 tablespoons of heavy whipping cream until reaching the desired consistency.