Preheat the oven to 425°F (220°C).
Prepare the vegetables: Peel and cut the sweet potatoes into 1- to 1½-inch pieces. Cut the broccoli into florets. Trim the asparagus and cut into pieces. Halve the cherry tomatoes.
Toss the vegetables: In a large bowl, drizzle the sweet potato and broccoli with 2 tablespoons of olive oil. Season with smoked paprika, garlic powder, salt, and pepper. Toss to coat evenly
Arrange on a sheet pan: Spread the sweet potato and broccoli on a large rimmed baking sheet in a single layer. Roast in the preheated oven for 20 minutes, stirring halfway through.
Prepare the softer vegetables: While the tougher vegetables roast, toss the asparagus and cherry tomatoes with the remaining 1 tablespoon of olive oil and season with salt and pepper
Add the softer vegetables: After 20 minutes, remove the sheet pan from the oven and add the asparagus and tomatoes. Spread them out evenly and return to the oven.
Roast for 8-10 more minutes: Continue roasting for another 8-10 minutes, or until the asparagus is fork-tender and all the vegetables are golden and crisp
Serve and enjoy: Remove from the oven, let cool slightly, and serve immediately