Preheat your oven to 350°F (175°C). Grease a cake pan.
In a mixing bowl, combine almond flour, sugar, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk together eggs, applesauce, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until well combined.
Pour the batter into the prepared cake pan.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.