How to Make It
Cook pasta according to package directions for al dente; drain. Transfer pasta to a large bowl.
Heat 1 tablespoon oil in a large skillet over medium. Add tomatoes, garlic, salt, and pepper and cook, stirring often, until tomatoes begin to soften, 2 to 3 minutes. Add zucchini and onion and cook, stirring often, until tomatoes burst and zucchini is almost tender, 3 to 4 minutes. Add corn and cook, stirring constantly, for 1 minute.
Add tomato mixture to pasta along with arugula, basil, and remaining 3 tablespoons oil and toss to combine. Serve warm or at room temperature topped with shaved Parmesan.