1. In a medium heatproof bowl, whisk egg yolks and 1/2 cup sugar until pale yellow and thick, about 2 minutes. In a medium saucepan, bring milk and salt to a bare simmer. Whisking constantly, slowly pour hot milk mixture into yolk mixture.

2. Pour yolk mixture back into saucepan. Cook over medium heat, stirring constantly with a wooden spoon, until mixture is just thick enough to coat back of spoon and hold a line drawn by your finger, 3 to 5 minutes.

3. Pour mixture through a fine-mesh sieve into a large bowl; discard solids. Let cool, stirring occasionally, about 20 minutes. Add cream, bourbon, rum, and cognac; cover and refrigerate overnight.

4. Whisk remaining 1/4 cup sugar and egg whites in a heatproof mixer bowl set over (not in) a pan of simmering water. Whisk until sugar is dissolved and mixture is warm (it should feel smooth between your fingers), 2 to 3 minutes. (For fully cooked eggs, a thermometer inserted into meringue should register 160 degrees.) Remove from heat. With a mixer on high speed, beat until stiff peaks form, about 5 minutes. Fold into eggnog.

5. Pour into glasses (or a punch bowl); top with a dollop of whipped cream and sprinkle with nutmeg.