Preheat your oven to 350°F (175°C).
Grease and flour a 9-inch round cake pan.
In a mixing bowl, combine flour, baking powder, baking soda, and salt.
In another bowl, mix sugar and butter until creamy.
Add applesauce and eggs to the sugar mixture, stirring until well combined.
Gradually add the dry ingredients to the wet mixture.
Fold in cinnamon and nuts, if using.
Pour the batter into the prepared cake pan.
Bake for 45 minutes, or until a toothpick comes out clean.
Let the cake cool before serving.