In a mixing bowl, whisk together flour, quick oats, baking soda, cinnamon, ginger, nutmeg and salt for 30 seconds, set aside.
In the bowl of an electric stand mixer, fitted with the paddle attachment, cream together 1/2 cup butter, granulated sugar and brown sugar until well blended. Mix in egg and vanilla extract. Set mixer on low speed and slowly add in flour mixture and mix just until combined. Stir in carrots, then fold in walnuts. Cover bowl and chill dough 1 hr 15 minutes. Preheat oven to 350 during last 10 minutes of chilling.
Bake in preheated oven 12 - 13 minutes until centers no longer look doughy. Allow to cool on baking sheet several minutes then transfer to a wire rack to cool. Cool completely then sandwich 2 cookies together with the cream cheese filling. Store in an airtight container in a single layer.
For the cream cheese frosting:
In the bowl of an electric stand mixer fitted with the paddle attachment, whip together cream cheese, butter and salt until smooth and fluffy. Stir in vanilla and powdered sugar and continue to whip until smooth and very fluffy.