Using a stand or a hand-held mixer, cream together the butter and sugar.
Add in the egg, vanilla extract, and juice from the three small mandarin oranges.
Slowly add in the flour and salt while mixing on low speed.
Using a plastic spatula or a spoon, fold in the cornstarch and baking soda.
Cover the mixing bowl with plastic wrap and let the dough chill in the refrigerator for 1-2 hours. (2 hours is best.)
Preheat oven to 350 degrees and line a baking sheet with parchment paper.
Using a heaping tablespoon, spoon the cookie dough onto the palm of your hands and roll into medium balls. Gently pat down on the cookie dough balls and place on the baking sheet.
Bake for 9-10 minutes. Let the cookies completely cool.
Prepare the glaze by creaming together the softened cream cheese and butter. Add in the powdered sugar ½ cup at a time.
Add in the heavy cream, juice from the mandarin oranges, and the zest.
Glaze the cookies and enjoy.