Preheat the oven to 350 degrees F and grease a standard 12-cup muffin tin or line with paper muffin cups (lightly grease the muffin liners with nonstick cooking spray - since the muffins are low in oil, it will help them not stick to the paper liners).
In a medium bowl, whisk together the butter or coconut oil, sugar, eggs, vanilla and applesauce. In a small bowl, combine the flour, baking soda, salt and cinnamon.
Stir the dry ingredients into the wet batter, mixing just until combined - it will look slightly lumpy; that's ok and better than overmixing which can cause the muffins to be dry and dense.
Spoon the batter evenly into the prepared muffin cups.
Bake for 13-15 minutes until the tops spring back lightly and the muffins are baked through; don't overbake or again, the muffins can be dry.
Remove the muffins from the tin and let them cool completely. Stir together the sugar and cinnamon for the topping. When the muffins are cooled, brush the tops with a bit of the melted butter or coconut oil and then immediately sprinkle lightly with the cinnamon and sugar (you may not need to use all of the cinnamon/sugar topping).