Preheat oven to 350° F
In a small saucepan over medium-low heat, simmer apple cider until it is reduced by half. Allow to cool.
In a large bowl, combine dry ingredients (flour, cinnamon, salt, baking powder, and baking soda). Mix and set aside.
In a stand mixer using the paddle attachment, cream together sugar, room temperature butter, and oil until a pale yellow color. This will take 3-4 minutes in a stand mixer but can also be done by hand.
Add eggs one at a time until incorporated.
To bowl of the mixer add remaining wet ingredients except for the apples.
Using a spatula, gradually add dry ingredients to wet until just combined.
Peel and dice apples into small pieces.
Add apples to muffin batter and gently fold in to combine.
Grease or line a muffin pan and fill each tin ¾ of the way full.
Bake for 20-22 minutes, or until a toothpick comes out clean.
Once they are finished cooking, place muffins on a rack until cool enough to work with, around 2-3 minutes. Keeping them warm helps the cinnamon sugar to stick.
In a bowl, melt butter. In a separate bowl, combine sugar and cinnamon.
Carefully dip the top of each muffin in melted butter shake off excess and then roll in cinnamon sugar to coat. Depending on whether you use liners or not, you can coat just the tops or the entire muffin.
Repeat for all muffins and enjoy warm.