Preheat the oven to 350°F. Spray an 8×8-inch baking pan with cooking spray.
In a large bowl, whisk together the gluten-free flour, baking soda, salt, cinnamon and nutmeg.
In a separate bowl, whisk together the applesauce, oil, egg, vanilla, lemon juice, brown sugar and granulated sugar.
Pour the wet ingredients into the dry ingredients and stir with a rubber spatula until just combined and no dry flour streaks remain. Stir in half of the chocolate chips.
Pour the batter into the prepared baking pan. Sprinkle the remaining chocolate chips on top
Bake for 25-30 minutes, until a toothpick inserted into the center of the cake comes out clean.
Remove from the oven and let cool completely before slicing.