Preheat oven to 350 degrees F. Prepare baking sheet by lining with parchment paper.
Place shredded carrots in a fine mesh strainer over a bowl. Sprinkle 3 tablespoons of brown sugar over carrots and stir to coat. Allow to sit for at least 15 minutes to make the carrots tender. You should get at least 1/4 cup of brown liquid that drains out. Discard liquid and set carrots aside.
Melt 4 tablespoons butter in medium sized bowl. Add 1 teaspoon orange zest and 1 teaspoon vanilla. When butter cools, but is still liquid, add egg. Stir well to combine.
In large separate bowl, combine flour, remaining 1/2 cup brown sugar, cinnamon, pumpkin pie spice, salt and baking soda. Stir to combine. Add sweetened carrots and egg mixture. Stir to combine (you may need to use your hands). Dough will be very sticky.
Divide dough into two equal portions. Using half the dough, make 14 balls of equal size on cookie sheet in three rows of 5-4-5. Use fingers to flatten each ball into circles that are about 1/4 inch thick.
Bake in preheated oven for about 12-14 minutes or until set. Allow cookies to rest on hot baking sheet for an additional 3 minutes before transferring to cooling rack. Repeat with second half of dough.
To make the filling, add 4 tablespoons cream cheese and 2 tablespoons of butter to bowl of stand mixture and beat with paddle on medium high speed for about a minute until light and fluffy. Add powder sugar, orange zest and vanilla. Scrape down sides and mix on low for about 30 seconds until well combined.
Match cooled cookies into pairs of like sizes. Either spread filling with a knife or add filling to a plastic bag and cut the corner off to squeeze it out. Distribute filling evenly onto 14 cookies, placing filling on flat side of cookie. Top with second cookie, flat side against cookie.