Wash, dry, and prepare the vegetables. If you are cooking the vegetables on the grill, you will want to keep chop them into larger pieces (or leave whole for items like mini bell peppers or mushrooms) so they don't fall through the grill grates. If you are using a grill basket, you can slice smaller.
Whisk together the olive oil, balsamic vinegar, garlic cloves, Italian seasoning, onion powder, salt, pepper, and parsley if using. Brush the mixture on the vegetables or toss them together in a large bowl.
Place in a grill basket or directly on the grill. If grilling directly, slice the veggies into larger pieces to make for easier flipping. Grill for about 5 minutes and either shake the grill basket or flip the veggies. Grill 4-5 minutes longer until tender. Season with additional salt and pepper if needed. Garnish with a drizzle of olive oil, fresh herbs, or cheese.