Preheat your grill to medium-high heat (around 400°F).
In a bowl, whisk together olive oil, balsamic vinegar, minced garlic, and thyme. Set aside half for dressing.
Brush the mushrooms, zucchini, peppers, and onion with the remaining marinade. Season with salt and pepper.
Place the vegetables on the grill, starting with the mushrooms. Grill for 4-5 minutes per side, or until they develop nice grill marks and become tender.
Remove vegetables as they finish cooking - mushrooms typically take 8-10 minutes total, while other vegetables might need 6-8 minutes.
Let the grilled vegetables cool slightly, then slice into bite-sized pieces.
Arrange mixed greens on a serving platter, top with grilled vegetables, and drizzle with the reserved dressing.