In a large pasta pot, cook pasta "al dente", 1 or 2 minutes less than the package instructions call for. Drain.
Meanwhile, slice off ends of zucchini and discard. Cut zucchini in half lengthwise. Using a mandoline, or carefully with a sharp knife, slice zucchini into very thin (about 1/8-inch) slices, trying to keep some skin on each piece for color. Stack slices and cut in half lengthwise. Reserve zucchini ribbons in a large bowl.
In the pasta pot, heat the olive oil over low-medium heat. Add garlic and cook until soft and translucent but not browned, about 1 minute. Add zucchini ribbons and 1/4 cup chicken broth, raise heat to medium-high and cook until zucchini is still somewhat firm but just cooked, about 3 minutes. Return pasta to pot and add remaining chicken stock; cook for 2 to 3 minutes, until liquid has mostly absorbed into the pasta. Add 1/4 cup of the Parmesan, parsley, basil, red pepper flakes, black pepper and toss to combine. Season with salt, to taste. Serve garnished with additional parsley, basil and the remaining 2 tablespoons of cheese.