Wash and dry all produce. Preheat broiler or grill to high. Bring farro and 31/2 cups water to a boil in a medium pot. Cook until tender, 25-30 minutes. Drain any excess water, then return farro to pot.

Trim ends from zucchini, then halve lengthwise. Cut each half into 4 long wedges. Toss with a large drizzle of oil. Season with salt and pepper. Pat chicken dry with a paper towel, then season all over with salt, pepper, and herbs de Provence.

Place zucchini and chicken on a lightly oiled baking sheet. Broil until zucchini is browned and chicken is no longer pink in center, 15-20 minutes, flipping halfway through. TIP: If grilling, grill zucchini and chicken over direct heat, turning occasionally, until lightly charred and cooked through, 15-20 minutes.

While zucchini and chicken cook, halve tomatoes lengthwise. Cut mozzarella into 1/2-inch cubes. Pick basil leaves from stems; discard stems. Thinly slice leaves.

Add tomatoes, mozzarella, and half the basil to pot with farro and toss to combine. Season with salt and pepper. In a small bowl, whisk together vinegar and 1 TBSP olive oil. Season with salt and pepper.

Divide farro mixture between plates. Top with zucchini, then drizzle with dressing. Add chicken to plate and sprinkle with remaining basil.