Preheat your oven to 350°F (175°C).
Grease a 9x13-inch baking pan with vegetable oil or butter, and optionally line the bottom with parchment paper.
In a large mixing bowl, whisk together the gluten-free all-purpose flour, baking soda, baking powder, ground cinnamon, ground nutmeg, and salt.
In another bowl, mix the granulated sugar, brown sugar, and vegetable oil until smooth. Then, add the unsweetened applesauce, eggs, and vanilla extract. Stir until fully combined.
Gradually add the dry ingredients to the wet ingredients. Stir gently until just combined. If using nuts or dried fruits, fold them in at this stage.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 30-35 minutes, checking for doneness with a toothpick.
Once baked, let the cake cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.