Step 1Beat the cream in a stand mixer (or in a medium chilled bowl, using a hand mixer), until stiff peaks form, about 3 minutes. Refrigerate the whipped cream until needed.
Step 2In a double boiler or in a heat-proof bowl set over simmering water, combine the egg yolks, one-half cup of sugar and Cognac. Whisking constantly, cook the egg mixture until it thickens slightly, is warm to the touch and looks satiny and white, 3 to 5 minutes. Cool the mixture by placing it over an ice bath and whisking, then refrigerate.
Step 3In the bowl of a stand mixer (or in a large bowl, using a hand mixer), whip the egg whites to stiff peaks along with the star anise, cinnamon, allspice, nutmeg and the remaining 2 teaspoons sugar. Set aside.
Step 4Fold the egg white mixture gently into the chilled egg yolks, then, again very gently, fold in the chilled whipped cream and milk, each a little at a time, until incorporated. Refrigerate until ready to serve. To serve, pour into chilled glasses or eggnog cups (or demitasses), with a pinch of allspice. The eggnog will keep for 1 day, covered and refrigerated.
Amaretto-apricot eggnog: Reduce the sugar to 2 tablespoons, to be cooked with the yolks (no sugar for the egg whites). Substitute three- fourths cup amaretto liqueur and one-fourth cup apricot liqueur for the Cognac. Omit the spices. Garnish: grated orange zest.
Nut brittle nog: Whisk one-fourth cup smooth peanut butter into the milk before incorporating. Substitute one-half cup vodka and one-half cup hazelnut liqueur for the Cognac. Spice with 1 teaspoon vanilla, one-half teaspoon almond extract, one-fourth teaspoon cinnamon and one-eighth teaspoon ground nutmeg. Garnish: a bit of ground nutmeg.
Wry vanilla eggnog: Substitute dark brown sugar for the sugar; don't add sugar to the egg whites (use only the one-half cup for the yolks). Substitute rye whiskey for the Cognac. Spice with 1 scraped vanilla pod. Garnish: nutmeg.
Scotch 'n' honey nog: Substitute 2 tablespoons chestnut honey for the total sugar (add to the egg yolks) and a Scotch for the Cognac. Omit the spices. Garnish: a swirl of chestnut honey.
Rum-coco nog: Don't add sugar to the egg whites (use only the one-half cup for the yolks). Substitute dark rum for the Cognac and 2 cups coconut milk for the milk. Spice with one-fourth teaspoon vanilla, one-half teaspoon ground cinnamon and a pinch of ground allspice. Garnish: toasted coconut.
Pink nog-tini: Don't add sugar to the egg whites (use only the one-half cup for the yolks). Substitute three-fourths cup gin (preferably Plymouth), one- fourth cup sweet vermouth, one- eighth cup maraschino liqueur and one-eighth cup grenadine for the Cognac, and one-half teaspoon almond extract for the spices. Garnish: a maraschino cherry sliver.
Naranja nog: Don't add sugar to the egg whites (use only the one-half cup for the yolks). Substitute three-fourths cup tequila (preferably anejo), one-fourth cup orange liqueur, and 2 dashes orange bitters for the Cognac. Spice with 1 teaspoon vanilla, one-eighth teaspoon cloves and one-fourth teaspoon ground cinnamon. Garnish: an orange twist.