Bring a large pot of lightly salted water to a boil. Cook pasta in boiling water until tender yet firm to the bite, 8 to 10 minutes. Drain.

Fill a medium saucepan with lightly salted water. Add zucchini and bring to a boil; cook until zucchini is tender, about 3 minutes. Drain.

Meanwhile, heat olive oil in a large skillet over medium heat. Sauté garlic and red pepper flakes in hot oil until fragrant. Add zucchini and parsley. Cook, stirring occasionally, until parsley is wilted.

Add pasta and toss until well combined. Sprinkle with cheese. Season with salt and pepper.