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Bring a large pot of salted water to a boil. Once boiling, add rigatoni to pot. Cook, stirring occasionally, until al dente, 9-11 minutes. Reserve 1 cup pasta cooking water (1 1⁄2 cups for 4 servings), then drain.
Meanwhile, wash and dry produce.
Halve, peel, and finely dice shallot. Peel and mince or grate garlic. Trim and grate zucchini on the largest holes of a box grater.
Place zucchini in the center of a clean kitchen towel. Gather into a tight bundle and squeeze over the sink to remove as much liquid as possible. TIP: Alternatively, place grated zucchini in a fine-mesh strainer and press down with a spatula.