Heat the oven to 350°F and arrange a rack in the middle.
Pulse the gingersnaps in a food processor until finely crushed. (Alternatively, you may place cookies in a large, sealable plastic bag and crush them with a rolling pin. You should have about 1 cup of crumbs.) Add butter and pulse until evenly combined.
Press mixture into the bottom of a 9-inch springform pan, wrap the bottom of the pan with aluminum foil, and bake until golden brown, about 12 to 15 minutes. Place crust on a wire rack to cool slightly, at least 15 minutes.
Meanwhile, combine cream cheese and sugar in the bowl of a stand mixer fitted with a paddle attachment and beat over medium speed until light and fluffy, about 3 to 4 minutes. Scrape down mixer bowl, add eggs and egg yolk, and beat until eggs are fully incorporated. Scrape down mixer bowl, add eggnog, vanilla, nutmeg, and salt, place mixer on low speed and mix until just incorporated.
Pour the filling over the crust and tap to remove any bubbles. Return the cheesecake to the oven and bake until edges are slightly puffed and filling is set everywhere but the center 3 inches, about 40 to 45 minutes. Turn off oven, prop oven door open a few inches, and let cheesecake cool down in oven, about 20 minutes.
Remove cheesecake from oven, run a knife around the perimeter of the cake, and let cool to room temperature. Refrigerate until ready to serve.
Beverage pairing: Wenzel Riesling Beerenauslese, Germany. Eggnog is filled with spice, sweetness, and a little sharpness, just like a good late-harvest German Riesling. But the amazing thing about the sweet styles of Riesling is their amazing acidity, which will add a refreshing zing to this rich cheesecake.
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