Cook the pasta according to the package directions. Reserve 1 cup of the cooking water, drain the pasta, and return it to the pot.
Meanwhile, heat the oil in a medium skillet over medium-high heat. Add the zucchini, ½ teaspoon salt, and ¼ teaspoon pepper.
Cook, stirring, until the zucchini is tender and any liquid has evaporated, about 5 minutes.
Stir in the garlic and cook 1 minute more.
Add all but 2 tablespoons of the cheese to the pasta. Add the reserved cooking water, ¾ teaspoon salt, and ¼ teaspoon pepper. Stir until creamy.
Serve the pasta topped with the zucchini, lemon zest, and remaining 2 tablespoons cheese.