For the cupcakes: Preheat the oven to 350 degrees F. Line regular sized cupcake pans with 24 liners. Beat the butter and sugar at medium speed with an electric mixer fitted with a whisk attachment until light and fluffy.
Add the eggs, 1 at a time, beating after each addition. In a food processor, combine the sweet potatoes, apple cider, and vanilla. Blend until smooth. Put aside. In a bowl, combine flour with remaining dry ingredients.
Whisk until blended.
Add the flour mixture to the sugar mixture, alternating with the sweet potato mixture. Beat at low speed just until blended after each addition. Fill the cupcake liners three-quarters full with batter.
Bake until golden brown, 22 to 24 minutes.
Remove from the pan immediately. Cool completely. For the cider reduction: In a medium saucepan, bring the cider to a boil, add the vanilla bean, and cook until the cider reduces to about 2 cups, 20 to 25 minutes.
Add the butter and sugar. Cook until the cider reduces to about 1 1/2 cups, stirring occasionally, about 10 minutes.
Transfer the mixture to glass bowl. Cover. Refrigerate for at least 3 hours, or until reduction is cooled completely. Can be made up to 3 days in advance. Reserve half for the Marshmallow Cream Frosting and half for assembling the cupcakes. For the marshmallow frosting: In a mixer fitted with a paddle attachment, beat the butter until smooth and creamy, scraping down the bowl occasionally, about 2 minutes.
Add the Caramel Cider Reduction and beat until incorporated.
Remove the bowl from the mixer and fold in the marshmallow creme until incorporated. For the pecans: Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Melt the butter in a bowl in the microwave. Coat the chopped pecan with butter.
Pour onto the prepared baking sheet and toast in the oven for 5 minutes.
Drizzle a small amount of Caramel Cider Reduction over the top of each cupcake. Generously frost each cupcake with Marshmallow Frosting and sprinkle with Toasted Salted Pecans.
