Prep a cookie sheet with parchment paper or oil. Set aside until ready to use.
Peel and finely grate carrots. Measure, lightly packed, in a 1 cup measuring cup. Set aside.
In a large mixing bowl, combine butter, brown sugar, and granulated sugar. Beat until smooth and creamy.
Add the eggs and vanilla extract. Mix.
Add the baking soda, flour, salt, cinnamon, ground ginger, and cloves. Mix until just combined.
Stir in the finely grated carrots and chopped walnuts.
Scoop dough into balls and place them on the prepared baking sheet. Leave space between each cookie.
Bake for about 9-13 minutes or until lightly browned around the edges.
Let cool on the baking sheet for at least 5 minutes. The cookies firm up as they cool. Then transfer to a wire rack to cool completely before frosting.
For Cream Cheese Frosting:
In a large bowl, beat together room temperature butter and cream cheese until completely smooth.
Add vanilla and salt.
Gradually add the powdered sugar. Mix on low speed until combined (or it’ll fly up into your face and all over your kitchen… I speak from experience.). If you are using a hand mixer, add about a 1/2 cup of powdered sugar, mix on low, add another 1/2 cup of powdered sugar, mix on low again, and so on. Do this until everything is combined.
Once combined, increase to medium-high speed and beat until thick and creamy (about 1-2 minutes).
Frost cookies after they cool completely. Decorate as you wish! Tips are in the post above.