Preheat the oven to 350˚F. Line a large baking sheet with parchment paper.

Sift together the flour, cinnamon, ginger, nutmeg, salt and baking soda. Set aside.

To the bowl of a stand mixer fitted with the paddle attachment, add butter and brown sugar. Cream at medium speed for 2 minutes, or until combined. Add applesauce and mix until combined.

Beat in the egg and vanilla for 1 minute. Add the dry ingredients to the bowl and mix at low speed for about 30 seconds, or until only a few streaks of flour remain.

Remove the mixing bowl from the stand mixer and fold the carrots and pecans into the batter using a rubber spatula.

Using a 1.5 tablespoons-size spring loaded cookie scoop, scoop the cookies onto the prepared sheet pan, make sure the cookies are spaced about 1 ½ inches apart. Bake for 10-12 minutes, or until the cookies are golden brown around the edges and the centers are puffed and set.

Let cool for 2 minutes on the baking pans, then transfer to a cooling rack to cool completely. Repeat with remaining dough.

While the cookies cool, make the icing. To the bowl of a stand mixer fitted with the paddle attachment, add cream cheese and butter. Mix at medium speed for 2 to 3 minutes, or until creamy. Add powdered sugar, milk and vanilla. Mix until combined. You want the icing to be slightly runny, but firm enough to pipe. Add more milk as needed to reach desired consistency. Transfer to a piping bag or ziptop bag and trim the corner off. Pipe a drizzle of frosting on the cooled cookies and serve.