1. Heat butter and sugar in a saucepan over medium heat; stir until melted. Stir in cream, and bring mixture just to a boil; remove from heat, and stir in vanilla extract. Let cool completely; refrigerate until cold and thickened.
2. Combine ice cream, milk, and 3/4 cup caramel mixture in a blender; process until smooth. Pour half of remaining caramel mixture into glasses, coating sides. Top with ice-cream mixture; drizzle evenly with remaining caramel mixture. Sprinkle with a pinch of sea salt.