In a saucepan over medium heat, warm the cream and milk, stirring occasionally, until steam rises from the surface. Remove from the heat.
In a heatproof bowl, whisk together the egg yolks and sugar until blended. Slowly add the hot cream mixture, whisking constantly. Pour the mixture into the saucepan or into a double boiler and set over medium-low heat. Cook, stirring slowly and continuously with a wooden spatula or spoon, until the custard thickens and a finger drawn across the back of the spatula leaves a path, about 6 minutes; do not allow the custard to boil.
Pour the custard through a fine-mesh sieve set over a clean bowl and stir in the vanilla, caramel sauce and salt. Nestle the bowl in a larger one filled halfway with ice and water and cool the custard to room temperature, stirring occasionally. Refrigerate until chilled, at least 1 hour.
Transfer the custard to an ice cream maker and freeze according to the manufacturer's instructions. Transfer the ice cream to a chilled container, cover and freeze until firm, at least 3 hours or up to 3 days before serving. Makes about 1 quart.