For the Eggnog Cake

• First, make the cake. Position a rack in the center of the oven and preheat the oven to 350°F. Generously spray a 9 x 13-inch cake pan with cooking spray and line the bottom with parchment paper.
• Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt.
• Cream the butter and sugars. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugars. Beat on medium until light, fluffy, and doubled in volume, 3 to 4 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary.
• Add the eggs, oil, eggnog, and vanilla. Reduce the mixer to low and add the eggs one at a time, adding the next egg only after the previous one has been fully incorporated, scraping down the bottom and sides of the bowl after each addition.

  With the mixer on low, slowly pour in the oil, followed by the eggnog and vanilla, and beat until the mixture is smooth, 3 to 4 minutes.
• Add the dry ingredients. Gradually add the dry ingredients and beat until just combined. Scrape down the bottom and sides of the bowl once more, and beat on low for an additional 30 seconds.
• Assemble and bake the cake. Pour the batter into the prepared pan. Bake for 40 to 45 minutes, or until the top of the cake bounces back when gently pressed. A skewer inserted into the center of the cake should come out with a few crumbs attached.
• Cool the cake. Cool completely in the pan on a wire rack before frosting.
• Once the cake is cool, make the frosting. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium-low until smooth and creamy, about 1 minute.

  Reduce the mixer to low and add the confectioners' sugar 1 cup at a time, beating until combined. Scrape down the bottom and sides of the bowl with a rubber spatula.

  Add the eggnog and salt for the frosting all at once and beat on low just to incorporate the liquid. Scrape down the bottom and sides of the bowl once more, then beat on medium-high until the frosting is creamy and smooth, 2 to 3 minutes.
• Assemble the cake. Use an offset spatula to spread the frosting on top of the cake. Then, use the spatula to make large, random sweeping motions across the frosting. The sweeping motions will create swirls. Garnish with sprinkles.
• Serve and store. Serve immediately, or cover loosely with plastic wrap and refrigerate for up to 3 days.