Reduce cider: Place apple cider in a saucepan over medium heat. Bring to a simmer and continue simmering until it reduces down to 1 cup. (This will likely take about 30 minutes at a low simmer. It can be done up to 5 days ahead and refrigerated until you're ready to use it). Let cool completely before cooking.

Preheat oven to 325°F / 163°C.

Spray a mini muffin tin (24 spaces) with nonstick cooking spray

In a large mixing bowl, combine flour, ½ cup sugar, baking powder, 1 teaspoon ground cinnamon, and salt.

In a second mixing bowl, whisk together reduced apple cider, egg, 4 Tablespoons melted butter, and vanilla extract until smooth.

Pour liquid ingredients over dry and stir just until everything is evenly combined. (The mixture should be fairly thin; be sure that there are no lumps.)

Fill prepared muffin tin with batter so that each space is about ¾ full.

Bake until the muffins are just set in the middle, 12 to 14 minutes.

Allow muffins to cool in the pan until cool enough to handle, about 10 minutes.

Put 4 Tablespoons melted unsalted butter in a small bowl. In a second small bowl, combine ¾ cup sugar and 1 teaspoon ground cinnamon.

Working with one mini muffin at a time, roll the top of the muffin in butter and then dip in cinnamon-sugar. Return the mini muffins to the pan to continue cooling completely.

Store in an airtight container at room temperature and serve within 24 hours.