Start by preheating your oven to 350°F. Combine the butter and both sugars and use a stand mixer or hand mixer to beat the butter and sugar mixture on medium speed. You'll need to scrape the bowl often; mix until creamy. Add the eggs and vanilla and mix again until everything comes together.

Next, combine the dry ingredients (flour, baking soda, cinnamon and salt) into a medium bowl and stir together. Then add the flour mixture to the wet ingredients and beat on low speed. Once the cookie dough is well mixed, stir in the grated carrots and chopped pecans.

Use a tablespoon or cookie scoop to drop the dough onto cookie sheets which have either been greased or covered with parchment paper.

Combine the powdered sugar, butter, cream cheese and vanilla in a large bowl. Mix at medium speed until the frosting is smooth and creamy. Each cooled cookie will take about two teaspoons of the frosting; reserve some of the frosting if you want to add more decoration to the top of the cookies. You can use the food coloring to green and orange frosting, scoop the frosting into bags and then pipe carrot designs on each cookie.