Line a baking sheet with parchment paper and set it aside.

In a mixing bowl, cream together the unsalted butter, granulated sugar, and light brown sugar until well combined.

Add the egg and mix until fully incorporated, scraping down the sides of the bowl halfway through mixing. Then, add the vanilla extract.

In a separate bowl, whisk together the all-purpose flour, cornstarch, baking soda, fine sea salt, ground cinnamon, ground ginger, and ground nutmeg.

Gradually add the dry ingredients into the wet mixture and mix on medium-low speed until just combined.

Slowly fold in the shredded carrots and chopped pecans, mixing just until combined. Do not overmix.

Using a 3-tablespoon cookie scoop, scoop out the dough and place balls on the prepared baking sheet.

Cover the dough balls with plastic wrap and place them in the freezer to set for at least an hour.

Preheat the oven to 350°F (175°C) and line another baking sheet with parchment paper.

Place the chilled dough balls on the new baking sheet, ensuring they are about 1 1/2 inches apart.

Bake the cookies for about 15 minutes or until they are lightly golden.

Once baked, remove the cookies from the oven and let them cool on the baking sheet.

For the icing, brown the salted butter in a small pan over medium heat, stirring constantly until it turns golden brown. Set the browned butter aside to cool.

In a bowl, cream together the room temperature cream cheese and cooled brown butter, adding the vanilla extract.

Gradually add the powdered sugar, one cup at a time, incorporating the ground cinnamon and fine sea salt with the last cup. Mix on medium speed for about 3 minutes until the icing is light and fluffy.

If the icing is too thick, you can add a splash of milk or heavy cream to reach your desired consistency.

Ice the cookies using a piping bag or by spreading the icing on top of each cookie. Garnish with chopped toasted pecans.