Melt the sugar. Place a saucepan or ladle with a thick bottom over medium heat. Pour the sugar into the saucepan and, when liquid begins to form around the edges of the saucepan after a couple of minutes, begin to stir the sugar with a spoon. Or you can move the ladle in gentle circular motions to capture as much unmelted sugar as possible. Melt all the sugar until it is amber in color and remove the ladle from the heat.
Add milk. Carefully pour the milk into the melted sugar, stirring constantly. If lumps of caramel form, return the saucepan to medium heat and continue stirring the mixture until the lumps are completely dissolved, without bringing it to a boil. Add vanilla and a pinch of salt and stir again.
Add butter to the caramel, remove the saucepan from the heat and stir well again. The caramel will thicken slightly as it cools, so immediately transfer it from the saucepan to a suitable container. It is best to store the finished caramel in a jar in the refrigerator.