Preheat oven to 350F. Line 2 baking sheets with parchment paper. Set aside.
Combine flour, cinnamon, ginger, salt, baking powder, baking soda and nutmeg in a medium bowl and stir with a fork to blend. Set aside.
Mix butter with sugars in a large bowl with an electric mixer until fluffy. Add eggs, one at a time, beating until combined. Then add vanilla and orange rind. Pour in flour mixture and stir until just combined. Fold in oats, carrots and dates.
Drop heaped tablespoons of mixture about 2 in. apart on prepared baking sheets and bake one sheet at a time for 15 min or until cookies are lightly browned on the bottom and cooked through. Let cool completely.
Beat together cream cheese, butter and icing sugar, and use about 1 tbsp to ice the bottom of half of the cookies. Then, sandwich iced cookie bottoms with dry tops.