Preheat your oven to 425F and brush the olive oil in an even layer over a baking sheet.
Trim and discard the tops and bottoms of the zucchinis and cut each one into three. Cut each piece into small batons and set aside.
In a small bowl, combine the cornstarch, 1/2 teaspoon of the salt, the garlic powder, and cayenne pepper. In a separate shallow bowl or dish, beat the eggs. Finally, combine the remaining salt, the panko, Parmigiano-Reggiano, and pepper in a third dish.
Dredge the zucchini fries in the cornstarch mixture and then quickly dunk them in the eggs. Finally, coat them with the panko mix and place them in an even layer on your prepared baking sheet, leaving some space in between each one. Give the tops of the zucchini fries a good spritz of cooking spray and bake them for 30 minutes, giving them a turn after 20 minutes or so.
These are best served hot with a side of mayonnaise or barbeque sauce for dipping.