Preheat the oven to 375 degrees.
Grate the carrots into a cheese cloth and ring out the excess carrot juice.
Using a stand mixer, beat together the butter and brown sugar until smooth.
Add the eggs in one at a time and mix on low.
Slowly add in the flour, cornstarch, baking soda, salt, and pumpkin pie spice. Mix until just barley combined.
Mix in the carrots and chopped walnuts.
Scoop 3 tbsp sized balls of cookie dough onto a cookie sheet.
Bake for 8-10 minutes until the tops of the cookies are slightly golden brown.
Allow the cookies to cool while you make the cream cheese frosting.
Beat together the cream cheese and butter until light and fluffy (about 5-7 minutes)
Slowly add in the powdered sugar and whip on low until all combined.
Add in the vanilla extract.
Scoop the cream cheese frosting into a piping bag and frost the cookies.