Stir together eggs, granulated sugar and salt in heavy Dutch oven. Gradually stir in milk. Cook over low heat 15 to 20 minutes, stirring constantly, just until mixture coats a metal spoon; remove from heat. Stir in vanilla. Stir together coffee and liqueur. Gradually stir coffee mixture into egg mixture; keep warm.
Just before serving, beat whipping cream and brown sugar in chilled large bowl with electric mixer on high speed until stiff. Gently stir 2 cups of the whipped cream into egg mixture.
Pour into mugs. Top with dollops of remaining whipped cream. Sprinkle with cinnamon. Serve immediately. Immediately refrigerate any remaining nog.