Adjust oven rack to center position and preheat oven to 425°F.

Peel the vegetables if desired, then cut into uniform pieces so they cook evenly. Smaller pieces will cook more quickly; larger pieces will take a bit longer to cook. If your vegetables still have some moisture after washing, be sure to pat them as dry as possible; the drier the vegetable, the better it will roast.

Transfer the vegetables to a large bowl. Add the oil, salt, and pepper and toss to combine. Add more oil if the vegetables still look dry or don't seem evenly coated.

Spread the vegetables out on to rimmed baking sheets, arranged by type. Make sure they are in a single layer with a little space in between. If they are too crowded, the vegetables will steam instead of roast -- use multiple baking sheets if needed instead.

Estimate your cooking time. In general, softer vegetables, like green beans and cauliflower, will cook in 10 to 20 minutes, and tough, hard vegetables, like winter squash and potatoes, will take 30 minutes or longer. Large pieces will also take longer to cook than smaller pieces.

Root vegetables (beets, potatoes, carrots): 30 to 45 minutes, depending on how small you cut them

Winter squash (butternut squash, acorn squash): 20 to 60 minutes, depending on how small you cut them

Crucifers (broccoli, cauliflower, Brussels sprouts): 15 to 25 minutes

Soft vegetables (zucchini, summer squash, bell peppers): 10 to 20 minutes

Thin vegetables (asparagus, green beans): 10 to 20 minutes

Onions: 30 to 45 minutes, depending on how crispy you like them

Tomatoes: 15 to 20 minutes

Roast the vegetables until tender. Place the vegetables in the oven and begin roasting. Check and stir the vegetables every 10 to 15 minutes. Continue roasting until the vegetables are easily pierced with a fork or knife and they are showing crispy, charred bits at the tips and edges.

Transfer the vegetables to a serving dish and taste; sprinkle with melted butter, Parmagiano Regiano, and more salt or pepper if needed.