Crack 8 eggs and separate the yolks from the whites; discard or reserve whites for another use, then let yolks sit at room temperature for 5 minutes.

Whisk the 8 egg yolks and 1/2 cup granulated sugar in a medium mixing bowl for 2 minutes until pale yellow and thick.

Pour 2 cups whole milk and 1 cup heavy cream into a heavy-bottomed saucepan and heat over medium heat, stirring occasionally, until steaming and reaching 160°F (about 5–7 minutes).

Remove saucepan from heat. Temper the egg yolk mixture by slowly whisking in one ladle of the hot milk mixture, then whisk in two more ladles, stirring constantly.

Pour the tempered egg mixture back into the saucepan with the remaining milk and cream, then cook over medium-low heat, stirring constantly, until mixture reaches 160°F and coats the back of a spoon (3–5 minutes).

Strain the custard through a fine mesh strainer into a clean bowl to remove any cooked egg bits.

Stir in 1 cup dark rum, 1/2 teaspoon vanilla extract, 1/4 teaspoon ground nutmeg, 1/8 teaspoon ground cinnamon, a pinch of ground cloves, and a pinch of sea salt.

Transfer the eggnog to a pitcher and refrigerate for at least 2 hours (up to 5 days) until well chilled and slightly thickened before serving.