Special equipment: four 12-inch wooden or metal skewers
Toss the mushrooms, bell pepper, zucchini and onion together with the olive oil, thyme, 3/4 teaspoon salt and pepper to taste and let stand at least 15 minutes and up to 1 hour.
Prepare a grill for medium-high heat. Thread the vegetables onto four 12-inch skewers, alternating vegetables.
Grill the vegetable kebabs, turning occasionally, until tender and charred in spots, about 25 minutes.
If using wooden skewers, soak the skewers in water for at least 30 minutes before using.