Prepare the applesauce: In a saucepan, combine cubed apples, brown sugar, ground cinnamon, and salt. Cook over low heat until apples are soft and sugar dissolves. Let cool. You will use 1 cup of this homemade applesauce.
Preheat the oven to 350°F (175°C) for 10 minutes. Prepare an 8x8 inch square pan, lined with parchment paper.
In a mixing bowl, combine gluten-free flour, baking powder, and baking soda. Mix well and set aside.
In a large mixing bowl, whisk together 1 cup of the prepared applesauce, eggs, and granulated sugar until the sugar is fully dissolved.
Gradually add the dry ingredients from the first mixing bowl into the wet ingredients in 3 parts, folding gently with a spatula after each addition.
Pour the batter into the prepared pan and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for a few minutes before transferring to a wire rack to cool completely.
Once cooled, you can prepare your desired frosting or ganache to top the cake.