Preheat the oven to 375°F and line a muffin tin with muffin liners or lightly grease it with butter.
In a medium bowl, add the flour, baking powder, baking soda, cinnamon, and salt, and mix with a spatula or wooden spoon to combine.
In a large bowl, add the melted butter, white sugar, and brown sugar and beat or whisk until smooth and well incorporated. Add the applesauce, egg, and vanilla extract, and whisk again to combine.
Transfer the dry ingredients to the wet ingredients and gently mix to combine using a spatula or wooden spoon, being careful not to overmix the batter.
Spoon the batter into the muffin cups, dividing it evenly to make 12 muffins.
Transfer the muffin tin to the oven and bake for 20-22 minutes until a toothpick inserted into a muffin comes out clean.
Once baked, allow the muffins to cool slightly in the muffin tin, then transfer them to a cooling rack to cool to room temperature.
For the cinnamon sugar topping, add the sugar and cinnamon to a small bowl and stir to combine. Using a pastry brush, brush the top of a muffin with melted butter (or dip the top of the muffin into melted butter), then dip the muffin (upside down) into the bowl of cinnamon sugar, move it around a little until the top is well coated with cinnamon sugar, then return to the cooling rack. Continue these steps until all of the muffins are coated with cinnamon sugar.
The muffins can be served immediately, stored at room temperature for 5 days, in the fridge for up to 7 days, or frozen for up to 3 months.