Preheat the oven to 350° F. Line cookie sheets with parchment paper, set aside.
Whisk together flour, baking soda, salt, cinnamon and nutmeg. Set aside.
In a bowl of a stand mixer (or using a hand mixer), mix together the butter, brown sugar and granulated sugar on medium-high speed until light and fluffy, about 3 to 4 minutes. Beat in vanilla, egg and egg yolk until light and creamy, about 1 minute. Scrape down sides when necessary.
Gradually add the flour mixture and shredded zucchini. Mix until just blended.
Use a medium cookie scoop to scoop dough and form into balls. Place on parchment lined cookie sheet and bake for 12 minutes. The edges will look lightly browned and the centers soft. Let the cookies cool on the cookie sheet for 3 minutes and then transfer to a cooling rack to cool completely.
For the frosting, beat cream cheese and butter until smooth and creamy. Add confectioner’s sugar and mix until well combined and fluffy. Mix in vanilla. If needed, add more for thinner consistency.
Use an offset spatula to frost cooled cookies. Add a sprinkle of cinnamon and serve.
Notes
Zucchini should be grated with the fine side of a box grater. Thoroughly remove the excess water by squeezing it out with a clean cloth.Cream cheese should be softened, but still cool to the such. Full-fat, block-style yields the thickest frosting. I do not suggest the variety from the tub.Store covered in an airtight container in the refrigerator for up to 1 week.Freeze the dough for up to 3 months or freeze baked cookies for up to 2 months. Wrap in plastic wrap to keep fresh and prevent freezer burn.