• Preheat oven to 350º F. Line cupcake pan with paper liners and set aside.

Make the cupcake batter.

• In a medium bowl, whisk together flour, baking powder, salt, and spices. Set aside.
  1 ⅜ cups cake flour, 1 ⅛ teaspoons baking powder, ½ teaspoon fine sea salt, ½ teaspoon ground nutmeg, ¼ teaspoon ground cinnamon
• In the bowl of a stand mixer (or in a large bowl using an electric hand mixer), cream the butter and sugar for 3 minutes until blended and smooth.
  ¼ cup unsalted butter, ¾ cup plus 1 Tablespoon granulated sugar
• Add egg and yolk and mix on low speed until blended. Then turn mixer up to high speed and beat for one minute.
  1 large egg + 1 large egg yolk
• Add oil and vanilla and beat until well blended.
  2 Tablespoons vegetable oil, 2 teaspoons vanilla extract
• With the mixer running on low speed, add one third of the flour mixture to the wet ingredients, stirring until blended. Add half of the eggnog, continuing to stir until combined. Add another third of the flour mixture, followed by the remaining eggnog, and then the final third of flour mixture, blending slowly between each addition. Gently fold in any final bits of flour, being careful not to over mix the batter.
  1 cup eggnog

Bake the cupcakes.

• Fill each well of the cupcake pan ⅔ full with batter (roughly 3 Tablespoons of batter per cupcake).
• Bake the cupcakes for 18-20 minutes, or until the tops sprig back when gently poked and a cake tester inserted into the center of a cupcake comes out clean or with just a few moist crumbs. Let the cupcakes cool completely.

Make the frosting.

• In the bowl of a stand mixer using the paddle attachment (or in a large bowl using a handheld electric mixer), beat butter on medium-high speed until smooth. 
  1 cup unsalted butter
• Add vanilla and salt and beat on medium-high speed until blended.
  2 teaspoons vanilla extract, 1 pinch fine sea salt
• Add sugar slowly – one cup at a time – beating well on medium speed and scraping the bowl often. When all sugar is added the frosting will be slightly dry. 
  3 ⅓ cups confectioners' sugar
• Add eggnog and beat on high speed until the frosting is light and fluffy.
  2 Tablespoons eggnog

Decorate the cupcakes.

• Add the frosting to a piping bag fitted with a piping tip. Pipe a tall swirl of frosting onto each cupcake.
• Sprinkle a bit of ground nutmeg over the frosted cupcakes and garnish them with a cinnamon stick (optional).