Melt butter in a small saucepan over medium heat. Add sugar. Bring to a gentle boil, whisking occasionally. Cook for 3 min. Stir in vanilla. Remove from heat and let stand 1 min. Whisk in cream until sauce is smooth. Stir in 1 tbsp rum or scotch just before serving.
Whisk 1 cup boozy caramel with 1 egg yolk and 2 tbsp cornstarch in a medium bowl. Set aside. Bring 2 cups milk to a boil in a medium saucepan. Reduce heat to medium-low. Gradually whisk in caramel mixture. Cook, whisking constantly, until thickened, 2 min. Remove from heat. Serve warm or cold.