Cook the pasta according to the package directions. Reserve ½ cup of the cooking water; drain the pasta and return it to the pot.
Meanwhile, heat the oil in a large skillet over medium heat. Add the broccoli, bell pepper, zucchini, garlic, ½ teaspoon salt, and ¼ teaspoon black pepper and cook, tossing occasionally, until tender, 8 to 10 minutes.
Add the vegetables, basil, and reserved cooking water to the pasta and toss to combine.