Preheat oven to 350°F and line 2 cookie sheets with parchment paper.
In a stand mixer fitted with paddle attachment or a large mixing bowl and hand mixer, cream together the softened salted butter, brown sugar and white sugar until light and fluffy and scraping sides as needed. This takes about 2-3 minutes.
While the butter and sugars are mixing, shred the carrots. Shred them fine and then pat with paper towels to get rid of any excess moisture.
Next, add the eggs, one at a time, and beat well after each egg. Then beat in the vanilla extract.
Now, add the dry ingredients: cinnamon, baking soda, baking powder, salt, and all purpose flour. Mix on low just until incorporated.
Stir in the shredded carrots and up to one cup of any additions, or mix in on low speed until evenly incorporated.
Using a ⅓ cup or 3.25 oz scoop, place 6 even cookie dough scoops on each prepared sheet pan. Roll and slightly flatten the cookie dough to look like thick hockey pucks.
Bake cookies, one pan at a time, on center rack for 15-17 minutes or until edges are lightly golden and the centers no longer look wet.
Let cookies cool on pans for 10 minutes. Then remove cookies to wire rack and cool completely.
While the cookies are cooling make the cream cheese frosting.