Beat the softened butter until it is light and fluffy. In a separate bowl, mix together the cornstarch, powdered sugar, and flour. Slowly add the dry ingredients to the butter and mix until moistened. It may take a couple of minutes for it to start to come together. You can check if it is moist enough by pinching some dough with your fingers. If it holds together, it is ready. If it is still too dry, add a teaspoon of milk.
Use a small cookie scoop (about 1 tablespoon) to shape the cookies. Place them on a parchment lined baking sheet about 2 inches apart. Make a small well in the center of the cookie using your thumb or finger.
Bake the cookies at 350 degrees for 10 minutes. Watch them carefully to avoid over baking. Remove them from the oven and transfer them to a cooling rack after 1 minute.
Cream Cheese Icing
Beat the softened cream cheese until smooth. Add the vanilla and the powdered sugar, a little at a time. Mix until incorporated. Add the food coloring to the frosting at this time, if desired.
Use a piping bag or a Ziploc bag with the corner cut off, to add the frosting to the well of the cookies. Top with sprinkles. Store these cookies in an airtight container in the refrigerator.