Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking pan and line the bottom with parchment paper.
Whisk the all-purpose flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and fine salt in a large bowl.
In another bowl, whisk the brown sugar, neutral oil, applesauce, whole milk, and vanilla extract until smooth. Stir in the grated carrots.
Fold the wet mixture into the dry ingredients just until combined, then fold in the chopped walnuts. Spread the batter evenly in the prepared pan.
Bake for 35 to 42 minutes, until the center springs back when gently pressed. Cool the cake completely in the pan.
Beat the cream cheese and softened butter until smooth and fluffy. Gradually beat in the powdered sugar, vanilla extract, and fine salt.
Spread the cream cheese frosting over the cooled carrot cake. Refrigerate for 30 minutes before portioning for cleaner servings.
