Combine the sugar and the butter in a medium size saucepan, over medium heat. When the butter has melted, stir to combine and continue stirring for 4 minutes. When the sugar and butter have combined and are bubbly, smooth and thick, remove from the heat. Very slowly, pour the cream into the hot caramel, whisking constantly. Whisk until smooth, making sure there isn't a great deal of caramel stuck on the bottom of the pan. (A little bit of caramel stuck to the bottom edges is fine.) Add the milk, vanilla, and salt. Whisk again until smooth. Cover and refrigerate until cold.
Process according to your ice cream machine's manufacturer's directions. Serve immediately for soft serve ice cream, or transfer to an airtight container and freeze for firmer ice cream. Enjoy!