Preheat oven to 350°. Line two baking sheets with parchment paper; set aside.
Combine carrot and 3 tablespoons brown sugar in a bowl; toss to coat. Place carrot mixture in a fine mesh sieve set over a bowl; allow to drain for 10 minutes. Discard liquid.
Place 2 tablespoons butter in a medium microwave-safe bowl and melt. Add oil, orange rind, ½ teaspoon vanilla extract, and egg; stir with a whisk until well combined.
Lightly spoon flour into a dry measuring cup and level with a knife. Combine flour, remaining brown sugar (about ½ cup), cinnamon, ¼ teaspoon salt, and baking soda in a large bowl; stir well with a whisk. Add carrot mixture and butter mixture; stir until just combined.
Drop dough by tablespoonfuls, 2 inches apart, onto prepared baking sheets for a total of 28 cookies (14 per baking sheet). Gently pat down dough to form 2-inch circles.
Bake at 350° for 10-12 minutes or until Carrot Cake Cookies are set. Remove pans from the oven and allow to rest for 3 minutes. Transfer cookies from pans to a wire rack and allow to cool completely.
Combine cream cheese, remaining 2 tablespoons butter, remaining ¼ teaspoon vanilla extract, and remaining ⅛ teaspoon salt in a medium bowl. Beat with a mixer at medium speed 3 minutes or until fluffy. Add powdered sugar and beat at low speed 1 minute or until well combined (do not overbeat).
Spread about 1 tablespoon icing on flat side of 1 cookie; top with another cookie, flat side down. Repeat procedure with the remaining cookies and filling.
Notes
NOTES FROM COOKING LIGHT:
Macerating the carrot with sugar helps to break down the carrot's tough fibers, ensuring that it will be tender after the short cook time.
After scooping dough onto baking sheets, gently pat it down so that cookies bake generally flat; aim for 2-inch circles.
When assembling the cookie sandwiches, press together gently so filling flattens and spreads all the way out to the edges.
NOTES FROM SAMANTHA:
If your carrot pieces are too thick, they won't have time to adequately soften in these cookies. Shredded carrots will work fine, but if you buy matchstick carrots in a package from the produce section, be sure to chop them finely before using in this recipe.
I used coconut oil (melted and cooled) with good results in lieu of another oil in this recipe, since that's what I typically use in my baking.
There is a definite undertone of orange from the zest, so if you don't care for citrus in your carrot cake, feel free to reduce or omit it.
I only got 12 total sandwich cookies (24 individual cookies) out of this recipe, despite using a tablespoon to measure them out. If you want to end up with 14 sandwich cookies by the end, I suggest using a scant tablespoon of dough per cookie.
The next time I make this recipe, I plan on substituting the all-purpose flour with whole wheat pastry flour for an even healthier variation.