In a medium saucepan, combine pudding mix, 1/4 teaspoon nutmeg, and Brown's egg nog; mix well. Cook over medium heat, stirring constantly, until thick and bubbly. Remove from heat, and stir in rum. Transfer mixture to a large bowl, cover, and refrigerate until thoroughly chilled.
In a medium bowl, whip the Brown's cream to soft peaks. Remove the cold pudding from the refrigerator, and beat until smooth; fold in whipped cream. Spoon into baked pie shell. Sprinkle additional nutmeg over the top for garnish. Refrigerate 4 hours, or until set.