Bring an 8-quart pot of well-salted water to a boil over high heat.
Heat the oil in a 12-inch skillet over medium heat. Add the onion and cook, stirring, until softened, about 2 minutes. Add the tomatoes, zucchini, bell pepper, garlic, 2 tsp. salt, and 1/2 tsp. pepper and cook, stirring occasionally, until the vegetables are barely tender, about 7 minutes. Pour in the heavy cream and simmer until it thickens and coats the back of a spoon, about 7 minutes. Stir in the cheese, basil, and lemon zest.
Meanwhile, boil the pasta according to package directions until al dente.
Drain the pasta and return it to the pot. Pour in the sauce and toss until the pasta is evenly coated. Season to taste with salt and pepper, sprinkle with additional cheese, and serve.