Preheat oven to 350 degrees. Line three miniature muffin or cupcake tins with liners. Set aside.
In the bowl of a stand mixer, beat together sugar and butter until light and fluffy, about 2 minutes. Add vanilla extract and vanilla bean paste. Add eggs one at a time, mixing after each addition.
In a medium size mixing bowl, whisk together cake flour, baking powder and salt. With mixing speed on low, alternate between adding wet ingredients (buttermilk and cider) and dry ingredients. Mix until just combined.
Scoop batter into prepared pans, filling each ⅔ of the way full. Place in oven and bake for 10-12 minutes, or until they become lightly golden brown on top. Remove from the oven and allow to cool in pans for 2-3 minutes before transferring to a wire rack to cool completely.
While cupcakes are cooling, to prepare the frosting, in the bowl of a stand mixer fitted with the whisk attachment, beat together butter for 1 minute until smooth. Add vanilla extract and salt. Gradually add powdered sugar, a half cup at a time, with mixing speed on low, add milk and sparking cider. Beat on medium-high speed for 2-3 minutes until frosting is light and fluffy (it should be relatively stiff). Add more powdered sugar if needed.
Notes
-This recipe can make standard size cupcakes, just adjust the baking time to 18-20 minutes.