Preheat the oven to 350°F (175°C) and grease a 9-inch round cake pan.
In a medium bowl, mix gluten-free flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a large bowl, whisk together the coconut sugar, oil, and vanilla.
Add applesauce to the wet ingredients and stir to combine.
Gradually add the dry ingredients to the wet ingredients, stirring until smooth.
Fold in the chopped apple.
Pour the batter into the prepared pan, smoothing the top.
For the topping: Mix brown sugar and cinnamon, then sprinkle over the batter.
Bake for 35-40 minutes or until a toothpick comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.