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, maple syrup, melted coconut oil, eggs, and vanilla until smooth and well combined.
In a separate bowl, combine both flours, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt. Whisk thoroughly.
Pour wet ingredients into dry ingredients and gently fold with a spatula until just combined. A few small lumps are fine. Fold in nuts if using.
Pour batter into prepared pan and spread into an even layer. Bake for 30-35 minutes until toothpick inserted in center comes out clean.
Cool in pan on wire rack for 15 minutes before turning out or cutting into squares. Serve warm or at room temperature.