Preheat oven to 350 degrees F. Line baking sheets with parchment paper; set aside.
In the bowl of a stand mixer, beat together your butter and sugars until light and fluffy. Add in your eggs and vanilla and beat until combined.
In a mixing bowl, whisk together your flour, cinnamon, nutmeg, cloves and baking soda.
Slowly add the flour mixture to the wet ingredients until combined. Mix in your carrots until blended.
Roll 2 Tbs of cookie dough into balls and place on baking sheet 2 inches apart. Gently press dough down with palm until flattened.
Bake for 15-20 minutes or until golden. Remove from oven and let cool on pan for 5 minutes before placing on wire rack to cool completely.
Meanwhile to make your frosting in a stand mixer by beating the butter and cream cheese until smooth.
Add in vanilla and mix until combined. Add in powdered sugar 1 cup at a time, mixing until just combined after each addition, until desired consistency is reached.
Spread onto cooled cookies and sprinkle with pecans and coconut.
Notes
If you don't have a stand mixer, a hand-held mixer will work fine.