1. In a bowl, whisk together 2/3 cup olive oil, soy sauce, vinegar, mustard, and garlic. Reserve 1/2 cup marinade for basting vegetables; pour remaining into a 1-gallon zip-lock plastic bag. Cut chicken into cubes and add to bag. Seal bag and turn to coat. Chill about 45 minutes.

2. Meanwhile, rinse zucchini, bell peppers, and mushroom caps. Slice zucchini lengthwise into 1/4-inch-thick strips. Stem and seed bell peppers; quarter lengthwise. Peel onion and slice crosswise into 1/4-inch-thick rounds. Brush vegetables with reserved marinade.

3. Lay vegetables and chicken (discard marinade) on a grill and close lid. Cook, turning once, until vegetables are slightly charred and chicken is no longer pink in center of thickest part (cut to test), 6 to 10 minutes total. Let cool a few minutes. Chop vegetables and chicken into 1-inch pieces.

4. Meanwhile, in a 6- to 8-quart pan over high heat, bring 4 quarts water to a boil. Add pasta, stir, and cook, uncovered, until barely tender to bite, 9 to 13 minutes. Drain.

5. In a large bowl, mix pasta with remaining 1/3 cup olive oil, parmesan cheese, half the chopped vegetables and chicken, and salt and pepper to taste. Top with remaining vegetables and chicken. Garnish with sliced basil.