Heat a large skillet over medium-high heat; cook and stir beef and garlic in skillet until beef is crumbly, evenly browned, and no longer pink, about 10 minutes. Drain and discard any excess grease. Stir in zucchini, tomato sauce, oregano, and basil; bring to a boil. Cover, reduce heat to medium-low, and simmer until zucchini is tender, about 15 minutes. Season with salt and black pepper.
Meanwhile, bring a large pot of lightly salted water to a boil. Cook shell pasta in the boiling water, stirring occasionally until cooked through but firm to the bite, 8 minutes. Drain.
Stir pasta and whole tomatoes into zucchini mixture, breaking up tomatoes with a spoon. Continue to simmer until heated through, about 25 minutes more. Toss with Parmesan cheese.