Step 1 Beat 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 2 In 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.