Preheat your oven to 425°F (220°C) and line a large baking sheet with parchment paper.
Cut the baby potatoes in half so they cook evenly and roast faster. Chop the remaining vegetables into similar-sized pieces.
Place the potatoes and harder veggies (like carrots) on the sheet first, since they need a bit longer to cook. Drizzle with half the olive oil and sprinkle with garlic powder, paprika, salt, and pepper. Toss well to coat.
Roast for 10 minutes, then remove the tray from the oven and add the rest of the vegetables — zucchini, peppers, onions, and broccoli. Drizzle with the remaining oil, toss again, and spread everything out evenly.
Return the pan to the oven and roast for another 20–25 minutes, tossing halfway through.
When the vegetables come out of the oven, sprinkle them with fresh herbs like thyme or parsley.