Preheat oven to 350 degrees.
In a large bowl, combine butter, oil, sugar, and brown sugar.
Mix until smooth and creamy.
Add in eggs, and vanilla extract. Mix everything together.
In a separate bowl, mix together flour, baking powder, and cinnamon.
In a measuring glass, mix together apple cider and applesauce.
Into the butter mixture, pour in half of the flour mixture. Stir until the flour is just combined.
Then pour in the apple mixture, and mix together.
After the apple mixture is fully mixed in, add in the remaining flour.
Pour the batter into a lined loaf pan, smoothing out the top.
In a small bowl, mix together sugar and cinnamon.
Sprinkle a generous amount of the cinnamon sugar to the top.
Bake for 40-50 minutes, until a toothpick inserted comes out clean.
Let cool slightly, and enjoy!