Yield: 16 servings.

For the syrup:

½ cup sweetened condensed milk
¼ cup whole eggnog (not light)
2 tablespoons spiced rum

For the cake:

2¾ cups cake flour
2½ teaspoons baking powder
½ teaspoon salt
½ teaspoon ground cinnamon
1 teaspoon ground nutmeg
¼ teaspoon ground cloves
2 sticks unsalted butter, softened
1½ cups granulated sugar
4 large eggs, room temperature
2 teaspoons vanilla extract
1 cup whole eggnog

For the icing:

4 sticks unsalted butter, softened
1 tablespoon spiced rum
½ teaspoon ground cinnamon
¼ teaspoon ground nutmeg
¼ teaspoon salt
4 cups powdered sugar, sifted
4 tablespoons whole eggnog

In a small bowl, stir together the condensed milk, eggnog, and 1 tablespoon spiced rum until well combined. Add the other tablespoon of spiced rum for a stronger flavor. Set aside.

Preheat oven to 350°. Lightly grease and flour three 6-inch round cake pans; set aside.

In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, nutmeg, and cloves until well combined.

Using an electric mixer, cream the butter and sugar until light and fluffy, about 5 minutes. Add the eggs one at a time, mixing well after each addition. Beat in the vanilla. On low speed, gradually add the flour mixture, alternating with 1 cup eggnog. Mix well after each addition. The batter will be thick.

Divide the batter evenly among the prepared cake pans. Use an offset spatula to spread batter evenly to the edges. Bake for 25 to 35 minutes or until a cake tester comes out clean.

Cool in the pans on a wire rack for 5 to 10 minutes. Using a fork or bamboo skewer, poke holes in the top of each cake. Drizzle or brush the rum syrup evenly over each layer. Let the layers sit in the pan for 5 minutes before removing from the pan and placing on a wire rack.

For the icing: Using an electric mixer, beat the butter on medium-high speed until light and fluffy. Add rum, cinnamon, nutmeg, and salt. Continue to beat until well incorporated. Add 2 cups of the powdered sugar until it’s mostly incorporated. Add the remaining sugar and mix for 3 to 5 minutes. Add the eggnog, one tablespoon at a time, until the icing reaches a soft, spreadable consistency.

Place one cake layer face up onto a serving platter. Spread a thin layer of icing evenly over the cake. Add the second layer face up and spread a thin layer of icing over the cake. Add the third layer, top side down, and frost the top and sides of the cake.