In a heavy bottomed saucepan combine the sugar and water over medium heat. Let dissolve. Add salt, strain, if necessary and bring back to a boil.
Add peanuts. Simmer them gently to let the water evaporate. Stir often to avoid burning. After a while the water should be completely evaporated and the nuts should be coated with crystallised sugar.
Turn the heat very low. Keep on stirring until the sugar dissolves again and starts to caramelise. All the while, stir, stir, stir. The nuts should eventually be covered in a coat of caramelized sugar.
Add the butter and the sesame seeds. Stir to coat nuts.
Pour the nuts out onto a greased baking tray or plate. Separate them carefully with two forks (they will be very hot!!!).
Let them cool then store them in a container with a tightly fitting lid.