Pare apples, cut into quarters and remove cores.
Cut each quarter in half crosswise, making 16 pieces total.
Measure flour into bowl. Gradually blend in 1 cup of the water using a whisk.
Add 2 teaspoons of the sesame oil. Beat until smooth. Brush remaining
1 teaspoon sesame oil over a serving plate. Set aside.
Place apple pieces in batter, turning to coat completely. Heat 3 cups
vegetable oil in wok over medium-high heat to 375 degrees F.
Using a slotted spoon, lift apple pieces from batter and place
in oil. Cook half of the pieces at a time until light brown, about
2 minutes. Drain on absorbent paper. Pour oil out of wok but do
not clean wok. Measure remaining 1 cup water and the sugar into
wok. Cook, stirring constantly, until mixture reaches about 235
degrees F on a candy thermometer, 10 to 13 minutes. Remove from
heat immediately. Mix in apples and sesame seeds. Transfer to the
oiled serving plate.
Place cold water and ice cubes in bowl.
Dunk apples in the ice water before eating.