Finely grate the carrots (I suggest using the finest grater), then place them in paper towels or cheesecloth and squeeze out as much liquid as possible. This is key for the right texture.
In a large bowl, combine the cold, cubed butter with the brown sugar and white sugar. Mix for 3–4 minutes, until the mixture is light and fluffy.
Add eggs and vanilla and mix for 1 minute longer.
Add the flour, cornstarch, baking soda, salt, and cinnamon. Mix just until the dough comes together. Do not overmix.
Cover and chill the dough for at least 30 minutes to help the cookies hold their thick shape while baking.
Preheat oven to 385 degrees. Divide the dough into large portions (about 5–6 oz each) and loosely shape into tall mounds. Do not flatten.
Bake at 385°F for 10–13 minutes, or until the edges are golden brown and the tops are pale and slightly soft. The cookies should look thick and slightly underbaked in the center.
Allow the cookies to rest on the baking sheet for 10–15 minutes before transferring. This helps them set and develop the perfect texture.
