In a small bowl, whisk egg yolks and sugar. In a small saucepan, heat eggnog over medium heat until bubbles form around sides of pan. Remove from the heat; stir a small amount of eggnog into egg yolk mixture. Return all to the pan, stirring constantly. Stir in the rum, vanilla and salt.
Transfer to six 6-oz. ramekins or custard cups. Place ramekins in a baking pan; add 1 in. of boiling water to pan. Bake, uncovered, at 325° for 25-30 minutes or until centers are just set (mixture will jiggle). Remove ramekins from water bath; cool for 10 minutes. Cover and refrigerate for at least 4 hours.