Preparation Cook orzo in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain. Rinse with cold water; drain well. Transfer to large bowl and toss with 1 tablespoon oil. Prepare barbecue (medium-high heat). Whisk 2 tablespoons oil and 2 tablespoons vinegar in small bowl. Brush zucchini and bell pepper with oil mixture, then sprinkle with salt and pepper. Whisk pesto, lime juice, remaining 3 1/2 tablespoons oil, and remaining 2 tablespoons vinegar in small bowl for pesto vinaigrette. Place shrimp in medium bowl. Add 2 tablespoons pesto vinaigrette; toss to coat. Grill zucchini and bell pepper until crisptender, about 3 minutes per side for zucchini and 4 minutes per side for bell pepper. Transfer to work surface. Sprinkle shrimp with salt and pepper; grill until charred and cooked through, 2 to 3 minutes per side. Place shrimp in bowl with orzo. Chop zucchini and bell pepper; add to bowl with orzo. Add remaining vinaigrette, tomatoes, sliced basil, and mozzarella; toss to combine. Season to taste with salt and pepper. DO AHEAD: Can be made 2 hours ahead. Cover; chill. Garnish with basil sprigs and serve cold or at room temperature.
Preparation Cook orzo in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain. Rinse with cold water; drain well. Transfer to large bowl and toss with 1 tablespoon oil. Prepare barbecue (medium-high heat). Whisk 2 tablespoons oil and 2 tablespoons vinegar in small bowl. Brush zucchini and bell pepper with oil mixture, then sprinkle with salt and pepper. Whisk pesto, lime juice, remaining 3 1/2 tablespoons oil, and remaining 2 tablespoons vinegar in small bowl for pesto vinaigrette. Place shrimp in medium bowl. Add 2 tablespoons pesto vinaigrette; toss to coat. Grill zucchini and bell pepper until crisptender, about 3 minutes per side for zucchini and 4 minutes per side for bell pepper. Transfer to work surface. Sprinkle shrimp with salt and pepper; grill until charred and cooked through, 2 to 3 minutes per side. Place shrimp in bowl with orzo. Chop zucchini and bell pepper; add to bowl with orzo. Add remaining vinaigrette, tomatoes, sliced basil, and mozzarella; toss to combine. Season to taste with salt and pepper. DO AHEAD: Can be made 2 hours ahead. Cover; chill. Garnish with basil sprigs and serve cold or at room temperature.