Preheat Oven to 350 degrees Prepare 2 baking trays with aluminum foil.
In a large bowl or the bowl of a stand mixer, add in softened butter and sugars. Using a paddle attachment or handheld mixer, mix until light and fluffy, about 2-3 minutes. Add in eggs, and beat until combined. Add the vanilla, and beat lightly until mixed in.
In a small bowl, combine flour, baking soda, salt, and spices. Add the flour mixture to the butter mixture, and mix until just combined.
Add carrots, and beat in lightly or fold in until combined.
Using a small cookie scoop or spoon, drop the mixture into rounds (about 1 - 1 1/2 tablespoons). Place 10 cookies per tray, you want to give them room to spread while baking.
Bake cookies for 12-15 minutes, until edges are golden and centers are just set. Let cool while you make the frosting.