Preheat oven to 425°F. Line a muffin tin with paper liners; set aside.
In a medium-sized mixing bowl, cream together the butter, vegetable oil, granulated sugar and brown sugar until smooth.
Add the eggs, beating to combine.
Mix in the baking powder, baking soda, cinnamon, nutmeg, allspice, ginger, salt, and vanilla.
On low speed, mix the flour into the butter mixture alternately with the apple cider and milk, beginning and ending with the flour and making sure everything is thoroughly combined. (So start with ⅓ of the flour, then all of the cider, then another ⅓ of the flour, then all of the milk, and finally the rest of the flour.)
Divide the batter evenly between the prepared muffin cups, filling them almost to the top.
Bake the muffins for about 15-17 minutes, or until they're golden brown and a toothpick inserted into the middle of one of the center muffins comes out clean.
Transfer the muffins to a wire rack.
When the muffins are cool enough to handle (but still warm), prepare the topping.
Place the melted butter in a small bowl. In a separate small bowl, stir together the sugar and cinnamon.
Brush the top of each warm muffin with the melted butter, then roll in the cinnamon-sugar.