Rinse, peel, and dice potatoes. In a small mixing bowl, add the diced potatoes, a tablespoon of oil, cumin, and smoked paprika. Stir or toss to coat.
Place a sheet of parchment or cooking spray over the baking sheet. Spread the potatoes over it.
Remove husk from corn and rinse. In the same bowl, coat corn with a tablespoon of oil, cumin, and smoked paprika. Place corn cobs on the potato baking sheet.
Rinse and chop the cauliflower, carrots, and brussels. In a separate mixing bowl, add the veggies, tablespoon of oil, salt, and black pepper. Stir or toss to coat.
Place another sheet of parchment on a second baking pan if you have one. Spread the veggies out over it. Try to space them out to improve results.