Preheat oven to 375 degrees F. Line two baking sheets with parchment paper.
Mix the flour, baking soda, salt and cinnamon together in a bowl.
Beat butter until creamy. Add both sugars, egg, and vanilla and beat just until mixed. Add the flour mixture and stir until fully blended.
Mix in carrots, nuts and raisins.
Drop 24 to 26 mounds of dough onto parchment lined baking sheets spacing at least 2 ½ inches apart.
Bake 1 sheet at a time on center rack for 12 -14 minutes or until edges are browned and centers appear set. Let cookies cool on baking sheet for about 4 minutes, then carefully transfer to a wire rack.
Prepare Filling. Beat together the softened butter and cream cheese, then gradually add sugar, beating and scraping bowl often. Beat in the vanilla.
Sandwich the icing between two cookies.