In a medium bowl, combine butter, sugar, and brown sugar. Beat until combined and creamy. Add eggs and vanilla making sure to mix well.
Add flour, baking soda, cinnamon and salt and beat to combine. Fold in carrots and chopped pecans and mix until combined.
Drop dough scoops onto greased cookie sheet. Bake for 10-12 minutes. Edges should be lightly browned. Let cool.
Make frosting by combing cream cheese, butter, powdered sugar and vanilla and beating until smooth. Reserve a little bit of the frosting for carrot design on top.
Frost cookies. Use food coloring to dye parts of the reserve frosting green and orange. Pipe carrot design onto cookies.