Preheat an oven to 425 F and arrange the oven racks so that they’re in the center of the oven. Let the oven preheat for at least 30 minutes.
Prepare the baking pan. Brush the sides of a 9 x 3 inch springform pan or cake pan with some of the butter. Press a 12x16” piece of parchment into the pan so that some of the parchment is above the edge of the pan. Brush the paper with more butter and then press another sheet of parchment paper the opposite direction so that all the sides are covered and there’s a parchment overhang around the entire cake pan. Try to smooth out the paper to the sides of the pan as best as possible. Brush the remaining butter all over the paper and up the sides. Set the prepared pan on a rimmed baking sheet and set aside. Having a sheet pan under the cake pan ensures that if there’s an overflow, it doesn’t end up on the bottom of your oven.
Whisk the cream and eggnog. In a large measuring cup, whisk together the cream, eggnog, and cornstarch until smooth. Set aside.
Beat the cream cheese and sugar together. Fit a stand mixer with the paddle attachment and beat the cream cheese and sugar on medium speed until the mixture is very smooth and the sugar is dissolved, about 3-4 minutes. Use a rubber spatula to scrape down the sides of the bowl and beat for another minute.
Mix in the remaining ingredients. Add the eggs one at a time, beating well between each addition. After you've added all the eggs, stop the mixer and scrape down the sides of the bowl again. On low speed, beat in the vanilla bean paste, salt, cinnamon, nutmeg, cloves, and rum until smooth. Scrape down the sides of the bowl again. On low speed, beat in the heavy cream and eggnog mixture. Make sure there are no lumps in the cheesecake batter.
Bake the cheesecake. Pour the cheesecake batter into the prepared pan and tap the pan on the counter several times to settle the batter. Bake for 40 minutes, until the top is deeply browned but the center is still very jiggly. If the top isn’t brown enough, set the oven to broil for 2 minutes. Remove the cheesecake from the oven and let it cool to room temperature on a wire rack or trivet, not on the stove. Chill for at least 2-4 hours before serving. Top with soft whipped cream and a light dusting of freshly grated nutmeg.