In a medium saucepan, bring milk, sugar, rice and salt to a boil, stirring frequently. Reduce heat and simmer about 20 minutes, stirring occasionally.
Lightly beat egg in a medium bowl. Gradually stir about a fourth of the hot milk mixture into the egg; return to pan, stirring constantly. Simmer for 20 minutes, stirring occasionally, until mixture is thick and rice is tender.
Remove from heat; stir in liqueur, vanilla and butter, stirring until butter melts.