Preheat the oven to 350°F (175°C) and line the bottom of three 8″ pans with parchment paper and grease the sides.
In a medium bowl, combine the flour, cinnamon, ginger, nutmeg, baking soda, and salt. Set aside.
2 cups (272 grams) Bob's Red Mill Gluten-Free 1-to-1 Baking Flour, 2 teaspoons ground cinnamon, 1 teaspoon ground ginger, 1/2 teaspoon ground nutmeg, 2 teaspoons baking soda, 3/4 teaspoon salt
In a large bowl, whisk the eggs and then add the sugar, applesauce, oil and vanilla and mix until combined.
4 large eggs, 1 1/2 cups (300 grams) granulated sugar, 3/4 cup (183 grams) unsweetened applesauce, 1/2 cup (118 ml) olive oil, 1 teaspoon vanilla extract
Add the dry ingredients to the wet and stir just until combined.
Then fold in the carrots, again only until combined.
14.5 oz (410 grams, about 3 1/2 to 4 cups) grated and peeled carrots
Bake for 19-22 minutes or until a toothpick inserted in the middle comes out clean.
Let cool for 5 minutes in the pans, and then turn onto a wire rack to cool.
Frost when completely cooled.
Prepare the frosting.
In a medium mixing bowl, beat the cream cheese and butter together with an electric hand mixer at medium speed until well combined. It's okay if it looks a little crumbly.
18 ounces (510 grams) full-fat cream cheese, 4.5 tablespoons (63 grams) unsalted butter
Gradually beat in the powdered sugar until totally combined and then beat in the salt and vanilla. Frost the cake with about 1/2 cup to 2/3 cup per layer and the remaining frosting on the sides. If you bake the cake and prepare the frosting in advance and want to refrigerate the frosting, note that it gets quite firm, like a cream cheese tart filling. If that happens, just bring it to room temperature, stir and then frost. The frosting firms up once refrigerated so if you want the softer frosting texture (rather than a cream cheese tart filling kind of texture), let the cake come to room temperature before serving.
1 1/2 cups (180 grams) powdered sugar, pinch salt, 3/4 teaspoon vanilla extract
Store the iced cake in the refrigerator for up to 3 days or the un-iced layers wrapped in plastic wrap at room temperature for up to 3 days.