Prep. Brush the grill grates with oil and preheat the grill to HIGH.
Prepare the vegetables. Meanwhile, brush the vegetables and the cheese with a bit of olive oil and season them with salt and pepper.
Grill. Place the eggplant rounds, the zucchini, the radicchio, and the cheese slices on the grill. Cover the grill and cook the vegetables and cheese, flipping them over as needed, for about 8 to 10 minutes, or until the vegetables are tender and slightly charred. The radicchio will be done before the rest of the veggies; just remove it from the grill and continue to cook the rest.
Make the dressing. In the meantime, in a large bowl, whisk together the honey, thyme, rosemary, lemon zest, lemon juice, garlic, salt, and pepper. Whisk in the remaining oil and then set aside.
Cut the vegetables. Remove the grilled vegetables from the grill and transfer them to a cutting board. Cut up the veggies and cheese into about 1 to 2-inch pieces and transfer them to the bowl with the honey dressing; gently toss to combine.
Serve. Taste for salt and pepper, and adjust accordingly. Garnish with parsley and serve.