Preheat a clean outdoor grill or grill pan to medium-high heat, about 400 to 450°F (205 to 230°C). Lightly oil the grill grates if needed to help prevent sticking.
In a medium bowl, stir together the parsley, garlic, oregano, red pepper flakes, red wine vinegar, 1/3 cup olive oil, and 1/2 teaspoon salt. Set the chimichurri aside while you grill the vegetables.
Place the zucchini, bell peppers, red onion, and mushrooms on a large tray. Drizzle with 2 tablespoons olive oil, then season with 1/2 teaspoon salt and the black pepper. Toss gently until coated.
Grill the vegetables in a single layer, working in batches if necessary. Grill zucchini and peppers for 3 to 5 minutes per side, onion rounds for 4 to 6 minutes per side, and mushrooms for 6 to 8 minutes total, turning occasionally. Cook until tender with browned grill marks; move vegetables to a cooler area of the grill if they brown too quickly.
Transfer the grilled vegetables to a serving platter. Spoon about half of the chimichurri over the warm vegetables and serve the remaining sauce alongside. Use a clean spoon for any sauce you plan to save.