Preheat oven to 425˚F/220˚C.
Place the potatoes, carrots, red onion, celery and garlic onto a sheet pan or into a large baking dish. Drizzle generously with olive oil and season well with salt and pepper. Place into the oven and bake for 20 minutes.
Carefully remove the sheet pan or dish from the oven and add the tomatoes, green beans, beans, stuffed pasta, dried oregano or basil, and red chili/pepper flakes. Drizzle with more olive oil and season again with more salt and pepper. Toss gently to combine.
Reduce the oven to 400˚F / 200˚C. Return to the oven and bake for another 20 to 30 minutes, until the vegetables are tender and the sauce is jammy.
Remove from the oven, give it a final season of salt and pepper and drizzle the vinegar over the top and give it a quick toss. Scatter over the parmesan or nutritional yeast, if using, and then drizzle with a bit more olive oil.