In a food processor or a hand grater/shredder, shred enough carrots for 2 cups. I use my Breville food processor, which has a large and small shredder attachment. The small shredder side was perfect for the size of the pieces I wanted for these cookies. Please DO NOT USE the store-bought bags of shredded carrots; they are dry and tasteless. They will draw the moisture out of your cookies.
In a bowl, weigh or measure the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg, running a whisk through to blend. In another bowl, weigh or measure the white and light brown sugars and set aside.
In a stand or hand-held mixer, cream the butter on medium speed for about 2 minutes. Then, add both sugars and mix on medium speed for about 3 minutes. Next, mix in the vanilla extract, applesauce, and egg. Scrape the bowl down. Turn the mixer speed to a low speed and slowly add the flour mixture until incorporated.
Scrape the bowl and then mix the shredded carrots through the cookie dough. Finally add the golden raisins and the chopped walnuts and blend them through the carrot cookie dough. I only refrigerate the cookie dough for as long as it takes to preheat my oven, about 10 minutes.
Preheat oven to 350°F (175°C or 180°C) and line 2 cookie sheet pans with parchment paper. I used a medium cookie scooper and scooped 12 mounds onto a pan. Bake for 12-14 minutes and then transfer to a cooling rack after you take them out of the oven. Wait until the cookies have cooled before starting the icing.