Bring a large pot of water with 2 teaspoons of the salt to a boil; add the fusilli. Cook until al dente.
Warm 1 tablespoon of the olive oil in a large skillet over high heat. Add the zucchini, scallions, pine nuts, lemon peel, red pepper flakes, and 1/2 teaspoon of the salt; cook, tossing frequently, until zucchini is well browned and tender, about 5 minutes.
Use a slotted spoon to transfer zucchini to a serving bowl. Remove lemon peel from pan. Mince 1/2 teaspoon of the peel and discard the rest. Squeeze half the lemon over the zucchini.
Turn heat to medium-high and swirl in remaining olive oil. Add the chicken, minced lemon peel, and remaining salt; cook, stirring, until golden, about 7 minutes.
Drain fusilli, reserving 1/4 cup of the cooking water. Add fusilli, zucchini, and reserved cooking water to skillet. Cook 1 to 2 minutes. Transfer to a bowl and top with the basil and, if using, Parmesan.