Gently heat the butter, sugar and cream in a saucepan, stirring until the butter has melted. Increase the heat and simmer for 5 minutes, stirring occasionally, until thickened and smooth.
Remove from the heat and stir in the vanilla seeds (reserving the pods), rum and a large pinch of salt.
Pour the sauce into small, sterilised jars. Slice the reserved vanilla pods into strips and add a piece to each jar. Leave to cool completely, then seal and chill. To serve, reheat the sauce and drizzle over ice cream or use as a dip for fruit.