Quarter the zucchini lengthwise and then cut in half. Place in a gallon resealable plastic bag along with the trimmed asparagus and green beans.
Add in the olive oil, garlic, thyme, oregano, salt, pepper and crushed red pepper. Seal and toss to completely coat the vegetables. Release any extra air from the bag and store in the refrigerator, along with the Parmesan, until ready to roast.
When ready to roast, preheat the oven to 425 degrees F. Remove the vegetable mix from the bag and spread it onto a sheet pan. Roast until the vegetables are tender and beginning to brown, 18 to 20 minutes, turning them halfway through the cooking time. Remove the vegetables from the oven and sprinkle the Parmesan over the top.