In a medium bowl beat butter and brown sugar with an electric mixer until light and fluffy. Add eggs and vanilla, beating well and scraping down the sides of the bowl.
In a small bowl, combine flour, cinnamon, baking soda, salt, nutmeg, and ginger.
Gradually add flour mixture to butter mixer, mixing just until combined.
Stir in oats and carrots, cover with plastic wrap and refrigerate for 2 hours.
Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
Drop by rounded tablespoonfuls on baking sheets, spacing 2 inches apart. Flatten them out slightly with your hand. They don't really spread out in the oven.
Bake 12 to 14 minutes, until lightly browned.. Cool on pan 2 minutes and remove to wire racks to cool completely.
Combine confectioners' sugar and sour cream in a small bowl. Stir until smooth. Drizzle on cookies. Place in a ziptop bag and snip the corner to get a more professional look.