For the Eggnog Cake
Prep the oven and pan. 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.
Make the cake. In a medium bowl, whisk together the flour, baking powder, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter, C&H® Granulated Sugar, and C&H® Light Brown Sugar. 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. 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. 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.
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 completely in the pan on a wire rack before frosting.
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 C&H® Powdered 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 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. Garnish with sprinkles. Serve immediately, or cover loosely with plastic wrap and refrigerate for 3 days.