Line baking sheet with parchment paper or silicone mat and preheat oven to 375º F.
In large bowl, beat beat both sugars, egg and butter with an electric or stand mixer. Mix until creamy.
Sift together all dry ingredients and add into wet ingredients. Beat until batter forms.
Add shredded carrots and mix thoroughly.
Using a cookie scoop (or a ¼ measuring cup), scoop mounds of batter on lined baking sheet, about 2 inches apart from each other.
Bake for 12-15 minutes and allow to cool before decorating.
To make the Carrot decorations:
Make buttercream by beating butter, icing sugar and milk.
Once ingredients are smooth and well-combined, scoop into a piping bag with a round tip attached. Frost center of each cookie.
Roll out 15-20 balls of orange fondant - about ½" in size. Shape them into cylinders. Press a small piece of green of fondant on the top of each orange piece.
Use a toothpick to score lines on the orange portion of your carrot, to give it texture.