Place a large bowl in a larger bowl of ice water and set aside. In a medium bowl, whisk together egg yolks and 1 cup sugar until pale yellow and thick, about 2 minutes.
In a medium saucepan, bring milk, vanilla bean, and 1/8 teaspoon salt to a bare simmer. Remove from heat. Whisking constantly, slowly pour 2 cups hot milk mixture into yolks. Whisking, slowly pour yolk mixture into saucepan. Cook over medium, stirring constantly with a wooden spoon, until mixture is thick enough to coat the back of spoon, about 3 minutes.
Pour mixture through a fine-mesh sieve into bowl in ice bath. Let cool, stirring occasionally, about 20 minutes. Cover and refrigerate eggnog base until chilled, about 1 hour.
Whisk brandy and cream into chilled eggnog base. In another large bowl, using an electric mixer, beat egg whites until soft peaks form. Gradually add 3/4 cup sugar and beat on high until stiff peaks form. Gently fold whites into eggnog base until blended. Serve eggnog sprinkled with nutmeg, if desired.
If you like, use a combination of brandy, bourbon, and dark rum in equal proportions. Don't have a vanilla bean? You can substitute 2 teaspoons pure vanilla extract. To skip raw egg whites: In step 4, omit the 2 cups cream that are added with the brandy. Substitute 3 cups heavy cream for whites and proceed as directed.