1. Combine first 3 ingredients in a medium saucepan; bring to a boil. Reduce heat; simmer 5 minutes or until cranberries pop. Place cranberry mixture in a blender or food processor; process until smooth. Strain cranberry mixture through a fine sieve over a bowl; discard solids.
2. Combine sugars and butter in a bowl; beat with a mixer at medium speed until well combined. Add egg yolks and egg, 1 at a time, beating well after each addition. Stir in cranberry mixture, cornstarch, and salt. Place mixture in the top of a double boiler. Cook over simmering water until a thermometer registers 160° and mixture thickens (about 10 minutes), stirring frequently. Remove from heat; let stand 5 minutes. Stir in liqueur. Cover and refrigerate up to 1 week.