Step 1

Heat grill to high. In a shallow baking dish, whisk together lemon zest and juice, garlic, shallot, and olive oil. Season with salt and pepper. Stir in chopped herbs.

Step 2

Season both sides of chicken with salt and pepper; drizzle lightly with olive oil. Brush grates with vegetable oil. Grill chicken, turning once, until charred in places and a thermometer inserted into thickest parts registers 160°F, 8 to 10 minutes. Transfer to dish and turn to coat with lemon mixture; tent with foil. Cover grill; return to medium-high heat.

Step 3

Drizzle vegetables lightly with olive oil; toss to coat. Season with salt and pepper. Grill, turning occasionally, until vegetables are charred in places and squash is crisp-tender, 6 to 8 minutes. Transfer to a plate. Let corn cool slightly, then strip kernels from cobs and transfer to a serving platter with squash, cheese, and herb leaves. Top with chicken; spoon more lemon mixture over top, if desired.