For the herby olive oil in a mixing bowl whisk together olive oil, parsley, lemon juice and garlic. Season lightly with salt to taste.
Preheat a gas grill over medium-high heat to about 425 degrees.
On one 18 by 13-inch baking sheet spread out red and orange bell peppers, corn, and red onions. Spray somewhat generously with cooking spray to coat each surface, season with salt and pepper.
Turn and coat opposite side of vegetables with cooking spray and season with salt and pepper.
On a second 18 by 13-inch baking sheet spread out zucchini, asparagus and mushrooms. Spray somewhat generously with cooking spray to coat each surface.
Turn and coat opposite side of vegetables with cooking spray and season with salt and pepper.
To the grill add the crisper vegetables first including bell peppers, corn, and red onions. Grill, covered, about 4 minutes per side.
Add the zucchini, asparagus, and mushrooms. Grill, covered, about 3 minutes per side until tender.
Transfer vegetables to a serving platter or return to baking sheet. Brush with the parsley oil mixture then sprinkle with the parmesan if using and serve.
