Preheat oven to 350F. In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, ginger, and nutmeg; set aside.
Using a standup mixer with a paddle attachment, cream the butter and sugars together until light and fluffy. Add in the egg and vanilla and mix. Add in 1/2 of the flour, then add in the carrots and the pecans. Mix lightly. Add in the remaining flour and mix until just incorporated. Scrape down sides of bowl if needed.
Spread out silicone liners and, with a cookie scoop or Tbsp., spoon out about 1 Tbsp. of cookie dough. Leave spacing of about 2" between cookies. Bake until browning on the edges but still soft to touch, 11-12 min. Cool on cookie sheet for 5 min. Then, cool completely on a cooling rack. If not icing immediately, place in a sealed container to prevent them from drying out.
For the icing. In a standup mixer with a paddle attachment, mix cream cheese until smooth, about 4 minutes. Mix in icing sugar and salt, add the milk, and mix until just combined and smooth. Place into an icing bag and decorate as shown. I used a Wilton #7 tip.
Notes
Adapted from Cooking Classy. See post for more tips and information.