Preheat oven to 350°. Line two baking sheets with a pieces of parchment.
In a mixing bowl, cream butter until fluffy, about 3 minutes. Mix in the cornstarch and sugar.
Add flour and mix until well combined.
Drop by small teaspoonfuls onto a prepared baking sheet. Using the bottom of a glass dipped in powdered sugar to prevent sticking, gently press down to flatten the dough.
Bake for 10-12 minutes.
Let sit for about a minute before transferring to wire rack to cool completely before frosting.
Cream Cheese Frosting
In a medium mixing bowl, beat the cream cheese until smooth, add the powdered sugar and vanilla, and thoroughly combine. Add food coloring if desired.