Whisk egg yolks and sugar together in medium bowl until blended. Gradually whisk in half and half. Pour into top pan of double boiler. Cook over simmering water, stirring constantly, until thick enough to coat back of metal spoon heavily (180 degrees F) 10-15 minutes. Strain through fine mesh sieve into medium bowl. Place bowl in larger bowl filled halfway with ice water. Stir 3 tabsp rum, vanilla and nutmeg into sauce. Let sauce cool, stirring occasionally, to room temp. Refrigerate covered until cold for 3-4 hours. Taste and add more rum if desired.