In a saucepan, combine sugar with 1 cup water. Bring to a boil over high heat, swirling occasionally to dissolve sugar.
Once sugar has dissolved, boil mixture, swirling occasionally (do not stir), until it has a medium amber color and honeylike consistency (if mixture appears to be browning too fast, lower heat to medium). Remove pan from heat and stir in butter and salt. Slowly pour in goat's milk (mixture will bubble furiously) and stir until smooth. Let cool slightly, then spoon over ice cream.