How to Make It
Prepare pasta in boiling water with 1 teaspoon salt according to package directions. Drain, reserving ½ cup cooking water.
Meanwhile, preheat grill to medium-high (400°F to 450°F). Toss together zucchini, squash, 1 tablespoon of the oil, ¾ teaspoon of the salt, and ¼ teaspoon of the pepper in a large bowl. Toss together shrimp and remaining 2 tablespoons oil, 1 teaspoon salt, and ¾ teaspoon pepper in a separate bowl. Arrange zucchini and squash in a single layer in a metal grilling basket. Place grilling basket on unoiled grates. Grill, covered, until slightly charred and tender, about 3 minutes per side.
Place shrimp directly on oiled grates. Grill, uncovered, until slightly charred and pink, about 2 minutes per side. Set aside.
Toss together zucchini, squash, shrimp, pasta, reserved pasta cooking water, parsley, basil, mint, and chives in a large bowl. Add butter, and toss until butter is melted. Serve immediately.