Prepare grill for direct-heat cooking over medium-hot charcoal (medium-high heat for gas), or heat a 2-burner grill pan over medium heat until hot.
Toss vegetables with 2 tablespoon oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Grill, turning occasionally, until tender, 6 to 8 minutes total. If using grill pan, grill in batches, 10 to 15 minutes per batch. Transfer peppers to a bowl and let stand, covered, 10 minutes.
Peel peppers and cut into 1-inch pieces. Cut zucchini crosswise into 1-inch pieces.
Whisk together vinegar, brown sugar, 1/4 teaspoon salt, 1/8 teaspoon pepper, and remaining 2 tablespoons oil in a large bowl. Stir in vegetables and basil. Let stand 15 minutes for flavors to blend.
