Brush the grill grates with oil and preheat grill to HIGH.
Brush the vegetables and cheese with a bit of olive oil and season with salt and pepper.
Place the eggplant rounds, the zucchini, radicchio, and the cheese slices on the grill.
Cover the grill and cook the vegetables and cheese, flipping them over as needed; cook for about 8 to 10 minutes, or until vegetables are tender and slightly charred. Radicchio will be done before the rest of the veggies; just remove it from the grill and continue to cook the rest.
In the meantime, in a large bowl whisk together the honey, thyme, rosemary, lemon zest, lemon juice, garlic, salt, and pepper. Whisk in remaining oil. Set aside.
Remove vegetables from the grill and transfer 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.
Taste for salt and pepper; adjust accordingly.
Garnish with parsley and serve.