Grate carrots and mix in a tablespoon of sugar. Set aside to macerate.
Mix sugars and cold butter until just combined.
Add egg and egg yolk to the butter mixture.
Add vanilla extract.
In a separate bowl, mix all dry ingredients (flour, cornstarch, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves).
Add dry ingredients to wet ingredients, ½ at a time, mixing until just combined.
Wring carrots as dry as possible to avoid overly cakey cookies.
Add carrots and other mix-ins (pineapple, nuts, white chocolate chips, and coconut). Mix until just combined.
Portion into mountains (approximately 4oz each for 12 cookies).
Freeze for 2-3 hours or until completely frozen.
Bake at 375°F for 15-18 minutes.
Let cool for 10-15 minutes before serving.
