In a dry skillet, toast the sesame seeds until golden. Set aside.
Squeeze lime juice over banana slices and set aside.
In a heavy saucepan, heat the sugar and water over a slow, even heat until the temperature reaches about 235*F. on a candy thermometer and the mixture forms threads. The syrup should be thick and bubbling.
Remove from the heat.
Butter a sheet of waxed paper.
Dip the banana slices into the syrup, place them on the waxed paper.