Pour 2 cups of fresh apple cider into a medium saucepan over medium heat. Bring to a gentle boil, then reduce heat to medium-low and simmer uncovered for 15–20 minutes, stirring occasionally, until reduced to approximately ½ cup. Cool completely before using; reserve 2–3 tablespoons separately for the frosting.
Preheat oven to 350°F (175°C) and line a 12-cup muffin pan with cupcake liners. Set aside.
In a large bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves until evenly combined. Set aside.
In a stand mixer fitted with the paddle attachment, beat softened butter, granulated sugar, and brown sugar on medium-high for 3–4 minutes until very pale and fluffy. Scrape down the bowl.
Add the eggs one at a time on medium speed, mixing 30 seconds after each addition, then mix in the vanilla extract. Scrape down the bowl.
On low speed, mix in the sour cream until just incorporated, then add the cooled apple cider reduction and mix briefly. The batter may look slightly curdled — this is normal.
Add the dry ingredients in 2–3 additions on the lowest speed, mixing just until no dry streaks remain after each addition. Do not overmix.
Divide batter evenly among the 12 liners, filling each about two-thirds full. Tap the pan gently, then bake for 18–22 minutes until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool cupcakes in the pan for 5 minutes, then transfer to a wire rack and cool completely — at least 30–45 minutes — before frosting.
Beat softened butter on medium-high for 3 minutes until very pale. Add sifted powdered sugar in 2–3 additions on low, then add reserved cider reduction, cinnamon, nutmeg, cloves, and salt. Beat on medium for 2 minutes until fluffy. Adjust consistency with heavy cream or additional powdered sugar as needed.
Pipe or spread the spiced buttercream onto the cooled cupcakes, then dust with ground cinnamon and garnish with a cinnamon stick or dried apple slice if desired.