Preheat your oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt. Set aside.
In a large bowl, cream the butter, granulated sugar, and brown sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the butter mixture, alternating with the apple cider and buttermilk, beginning and ending with the dry ingredients. Mix until just combined — do not overmix.
Divide the batter evenly among the cupcake liners. Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean. Let the cupcakes cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
In a large bowl, beat the softened butter until smooth. Gradually add the powdered sugar, mixing well between additions. Add the reduced apple cider, vanilla extract, cinnamon, nutmeg, cloves, and a pinch of salt. Beat until light and fluffy.
Once the cupcakes are completely cooled, pipe or spread the spiced buttercream frosting generously over the top of each cupcake.
Garnish with a sprinkle of cinnamon or a cinnamon stick for decoration, if desired. Enjoy these cozy, fall-flavored cupcakes!