Spiced Apple Cider Cupcakes
Make the cupcakes:
Heat an oven to 350° F.
In the bowl of a standing mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until it is light and fluffy, about 3 minutes.
Add the egg, baking powder, baking soda, and salt, and mix well to combine, about 1 minute.
Add the flour in 3 batches and the cider in 2 batches, alternating between the two and starting and ending with the flour.
Pour the batter into lined muffin pans; fill the cups about ¾ full. Bake for 20 minutes; a toothpick should come out clean. Let the cupcakes cool completely before frosting.
Make the frosting:
Put the egg whites and salt into the bowl of a standing mixer fitted with the whisk attachment.
In a small saucepan, bring the water and sugar to a boil. When the mixture reaches a boil, turn on the mixer and beat the whites and salt at medium-high speed until they hold soft peaks. Remove the saucepan from the heat.
With the mixer still running, pour the sugar mixture down the side of the bowl. Let the mixer run until the mixture is cool, about 10 minutes.
Once the mixture is cool, add the butter, ½ tablespoon at a time. After all the butter has been added, add the spices and rum. Beat for 1 more minute to incorporate. Frost cupcakes once they are cooled.