Preheat oven to 350°F (175°C). Grease a 9x9 inch square baking pan or line with parchment paper.
In a large bowl, whisk together applesauce, eggs, maple syrup, melted coconut oil, and vanilla until smooth and well combined.
In a separate bowl, combine flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Stir thoroughly.
Fold dry ingredients into wet ingredients using a spatula. Mix just until no flour streaks remain - do not overmix.
If using, fold in walnuts or raisins gently.
Pour batter into prepared pan and spread evenly with the back of a spoon.
Bake for 30-35 minutes until toothpick inserted in center comes out clean or with few moist crumbs.
Cool in pan for 10 minutes, then transfer to wire rack to cool completely before slicing.