Preheat oven to 350°F. Grease and flour two 8” round cake pans (or use floured nonstick cooking spray). Place a strip of parchment in the bottom of the pan that goes up the sides for easy removal.
Whisk salt, baking powder, baking soda, cinnamon, ginger, nutmeg, and flour in a medium bowl. Set aside.
Whisk eggs until beaten, then whisk in oil, vanilla, applesauce and both sugars. Whisk until combined, then add dry ingredients and stir with a spatula or wooden spoon until just combined, then stir in carrots.
Divide batter between the two pans. Bake for 40-45 minutes or until a toothpick comes out clean in the center. (Note: after about 30 minutes my cakes were browning a lot on top, so I reduced the oven temperature to 325°F. If you notice your cakes browning fast, you can lower the temperature as early as 20 minutes, and this may affect baking time a little. The cakes do get quite brown because of the brown sugar and spices, but the pans you use and your oven can cause it too.)
Let the cakes completely cool before removing from the pan and frosting.
To make the frosting: beat cream cheese and butter until smooth. Add powdered sugar, 1 cup at a time, until the mixture comes together, then add vanilla and salt. Beat until smooth, then stir in pecans.
To frost the cake: I made four layers by “torting” the cake. To torte each layer, place a ring of toothpicks around the middle at equal intervals, then slice the cake in half using the toothpicks as a guide. Layer cake on cake plate with the frosting, adding pecan halves on top for garnish. You can frost the sides if you want, or leave it naked as I have.
Store loosely covered in the refrigerator for up to 3 days.