Stir together milk, sugar and egg yolks in heavy medium-size saucepan. Heat over low heat, stirring constantly with wooden spoon, until mixture registers 180 degrees F on instant-read kitchen thermometer, 5 to 8 minutes; do not let boil. Mixture will thicken slightly, but will not coat spoon.
Strain mixture through sieve into bowl. Cover; refrigerate until well chilled, 3 hours. Stir in the heavy cream and vanilla.
Freeze mixture in ice-cream maker according to manufacturers directions. Transfer to bowl; place in refrigerator-freezer. Makes about 5 cups. (Nutrition facts are based on 1/2 cup.)