Combine eggnog, sugar, and salt in medium saucepan. Slowly whisk in cornstarch. Bring to a boil, stirring constantly, over medium heat. Boil for 1 minute. Remove from heat and stir in butter and bourbon. Let cool before refrigerating until thoroughly chilled.

For the dough: In bowl of an electric mixer fitted with paddle attachment, combine butter, sugar, salt, vanilla, and egg. Beat on medium-high speed until light and fluffy, scraping bowl as necessary. Reduce speed to low and gradually add flour, scraping bowl as necessary, until a soft dough forms. Divide dough into 2 portions, form into 1-inch-thick disks, and wrap in plastic wrap. Refrigerate for at least 15 minutes or until ready to use.

Heat oven to 350°. Portion dough into 1-inch balls and place on parchment-lined baking sheet. Use thumb to make a deep indentation in each cookie to hold custard after baking. Bake until light golden, 16–18 minutes. Transfer to wire rack to cool completely.

Fill each cookie with a dollop of cold eggnog custard. Dust with confectioners, sugar and sprinkle with nutmeg. Serve immediately.