Using a hand or stand mixer, cream together sugar and butter. Add eggs one at a time, mixing well. Add in applesauce and vanilla, mix.
In a separate bowl, sift together flour, baking powder and salt. Combine dry ingredients with wet and mix until incorporated. Spoon into muffin tin that has been coated with non-stick spray. Bake for 15 minutes (test for doneness with a toothpick inserted into middle of muffin.) Remove muffins from pan and cool.
Mix together sugar and cinnamon. Dip each muffin into melted butter then into cinnamon sugar. Makes 12 muffins.