Preheat your oven to 350°F (175°C) and prepare two 9-inch round cake pans with parchment paper.

In a large mixing bowl, combine gluten-free flour, baking powder, baking soda, cinnamon, nutmeg, ginger, allspice, and salt.

In a separate bowl, whisk together vegetable oil, granulated sugar, light brown sugar, vanilla extract, eggs, and applesauce until smooth.

Gradually add the dry ingredient mixture to the wet ingredients, stirring until just combined.

Fold in the shredded carrots and chopped pecans gently into the batter.

Divide the batter between the prepared cake pans and bake for 28 minutes.

Allow the cakes to cool in the pans for 15 minutes before transferring them to wire racks to cool completely.

Make the cream cheese frosting by beating cream cheese and unsalted butter until smooth, then add powdered sugar and vanilla extract.

On a serving platter, layer one cake with frosting, add the second layer, and frost the entire cake.

Chill the frosted cake in the refrigerator for at least 30 minutes before serving.