• Preheat the oven to 350°F. Grease and line two 9-inch cake pans.
• Combine 2 1/2 cups 1-to-1 gluten free flour, 300 grams, 2 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, 2 teaspoons cinnamon, 1/4 teaspoon nutmeg, 1/2 teaspoon ginger, 1/2 teaspoon allspice1/2 teaspoon salt in a large bowl. Whisk together to mix well.
• Add 1/2 cup vegetable oil, 1 cup granulated sugar, and 2/3 cup lightly packed light brown sugar to the bowl of an electric mixer. Beat on medium speed for 2-3 minutes. Scrape down the bowl.
• Add 1 teaspoon vanilla extract, then 3 large eggs, one at a time, mixing for 60 seconds between each addition.
• Turn the mixer to low speed and add half of the flour mixture followed by half of the 1/2 cup applesauce. Repeat with the remaining flour mixture and 1/4 cup applesauce.
• Remove the bowl from the mixer. Add 2 1/2 cups shredded carrots and 3/4 cup chopped pecans and fold together by hand until they are evenly distributed.
• Divide evenly among the cake pans and bake for 25-28 minutes or until the top springs back when gently pressed.
• Remove from the oven and cool in the pan for 10 minutes, then remove from the pan and transfer to a wire rack. Cool completely before frosting.

To Make the Frosting:

• Combine 8 oz cream cheese, and 1/2 cup unsalted butter, both softened to room temperature, in the bowl of an electric mixer. Beat on medium speed for 2-3 minutes until smooth and creamy. Scrape down the bowl.
• Add 5 cups powdered sugar, sifted, and 1 teaspoon vanilla extract. Start the mixer on low speed. Stir until the sugar is all incorporated. The mixture will resemble a thick paste.
• Turn the mixer to high speed and beat for 5 minutes, until the frosting is fluffy and lighter in color.

To Assemble the Cake:

• If necessary, level the cake rounds before frosting.
• Place the first cake round on a plate. Top with about 1⁄3 of the frosting. Spread over the cake round to the edges.
• Top with the second cake round. Spread about 1⁄2 of the remaining frosting on the top and sides of the cake, making a thin even layer.
• Chill the cake for 30 minutes.
• Remove the cake from the refrigerator and apply the remaining frosting into a decorative layer.
• Decroate the top and/or sides with 1/2 cup chopped pecans, if desired.