In a heavy bottomed pot 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 dissolve. Stir often to avoid burning. After a while the water should be completely evaporated and the nuts should be coated with crystallized sugar.
Turn the heat very low. Keep on stirring until the sugar dissolves again and starts to caramelize. 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 sheet pan or plate. Separate them carefully with two forks (they will be very hot!!!).
Let them cool and store them in a container with a tightly fitting lid.