Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners.
In a mixing bowl, combine applesauce, sugar, vegetable oil, eggs, and vanilla extract, and mix well.
In another bowl, whisk together flour, baking soda, baking powder, salt, and cinnamon.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
If using, fold in chopped nuts gently into the batter.
Evenly distribute the batter into the prepared muffin tin, filling each cup about 2/3 full.
Bake in the preheated oven for 20-25 minutes or until a toothpick inserted comes out clean.
Allow muffins to cool in the pan for 5 minutes before transferring to a wire rack.
Enjoy warm or at room temperature!
Store any leftovers in an airtight container.