Combine 1/3 cup cornstarch with the flour in a resealable plastic bag and shake it well;rinse the eggplant, drain it and shake it in the cornstarch mixture in batches, placing it in a large bowl as it's coated.
In a wok heat 1 cup of the oil over high heat until hot but not smoking; add pine nuts with a strainer, removing it as soon as pine nuts are golden; drain on paper towels.
Add another 1 1/2 cups of oil to the wok and heat to 375° on a deep fat thermometer; fry eggplant in three batches, stirring and turning until golden, about 6 minutes; drain 5 minutes in a colander set over a bowl, then pour into a serving bowl.
Stir the soy sauce, sugar, remaining teaspoon of cornstarch and the broth in a small bowl until cornstarch is dissolved.
Remove the oil from the wok, wipe it dry with a paper towel and add the final 1 1/2 tsp of oil; heat and when hot stir-fry the gingerroot, scallion, garlic and chili sauce until fragrant, about 30 seconds.
Stir the soy sauce mixture and add it to the scallion mixture; stir and bring mixture to a boil; add sesame oil and pine nuts; stir and pour over eggplant.