Preheat your oven to 400F. Toss the root vegetables and red onion with the vegetable oil and arrange them on two parchment or foil-lined baking sheets. Sprinkle them with salt and pepper. Roast the vegetables for 35-40 minutes, or until browning gently and tender.
Meanwhile, boil the pasta according to package instructions. Drain.
When the vegetables are ready, heat the olive oil in a very large, deep skillet over medium heat. Add the shallot and garlic. Cook, stirring frequently, till the shallot is clear and tender (about 4-5 minutes). Add the pasta, roasted vegetables, broth, and vinegar. Warm everything through in the pan, stirring as you go. Stir in the arugula and allow it took until it's gently wilted. Taste and add salt and pepper to taste, along with an extra splash of vinegar if desired. Serve right away, with parmesan if you like.
You can substitute a few tablespoons of vegetable broth if you wish, and/or roast the veggies without oil.