Preheat the oven to 350 degrees F (175 degrees C). Grease or line a 9-inch cake pan with parchment paper.
Whisk flour, nutmeg, baking soda, baking powder, salt, cinnamon, and cloves together in a medium bowl. Set aside.
Beat sugar and butter together in a large bowl with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition. Mix in vanilla extract. Add 1/3 of the flour mixture and stir until just combined. Pour in 1/2 of the cream and 1/2 of the spiced rum and mix until just combined. Continue alternating adding the flour mixture, cream, and spiced rum until combined. Do not overmix. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 35 to 40 minutes. Allow to cool for 5 minutes in pan before removing to a serving platter.
While cake is baking, make the eggnog sauce. Whisk egg yolks and sugar together in a small bowl. Mix in flour, cornstarch, vanilla extract, and salt; mixture will be very thick.
Combine milk and eggnog in a medium saucepan over medium-low heat. Heat until just barely simmering. Slowly pour 1/2 of the hot milk mixture into the egg yolk mixture, whisking constantly. Pour egg yolk mixture back into the saucepan with the milk and eggnog; whisk to combine. Continue cooking, whisking constantly, until thickened, about 2 minutes.
Pour sauce through a fine-mesh sieve into a heat-safe bowl. Let cool slightly, then place a piece of plastic wrap directly onto the surface of the sauce to prevent a skin from forming.
While cake is still very warm, poke holes all over using the handle of a wooden spoon. Slowly pour eggnog sauce over cake and let soak in, spreading sauce over the cake with a spatula if necessary. Allow to cool completely, at least 30 minutes.
Make eggnog whipped cream just before serving. Beat cream, eggnog, powdered sugar, vanilla extract, and salt together on high speed in a medium bowl until stiff peaks form.
Place several dollops of whipped cream on the completely cooled cake. Top with freshly grated nutmeg.
