Preheat the oven to 425°F (220°C). Wash all vegetables. Peel and cut carrots into 1/2-inch coins or sticks (about 3 cups). Remove seeds and membranes from bell peppers and cut into 1-inch pieces (about 1 cup each). Trim ends of zucchini and cut into 1/2-inch rounds or half-moons (about 2 cups). Peel red onion and cut into 1-inch wedges (about 1 cup). Cut broccoli into bite-sized florets (about 2 cups). Halve small baby potatoes so pieces are roughly the same size as the other vegetables (about 2 cups).

Season and Toss

Combine oil and seasonings

In a large mixing bowl, whisk together 3 tablespoons extra-virgin olive oil, 3 teaspoons minced garlic, 1 teaspoon dried rosemary, 1 teaspoon dried thyme, 1 teaspoon smoked paprika, 1 teaspoon sea salt, and 1 teaspoon freshly ground black pepper until combined.

Coat vegetables

Add all prepared vegetables to the bowl. Using tongs or clean hands, toss thoroughly so each piece is evenly coated with the oil and seasoning mixture. If you prefer slightly crisper vegetables, reserve 1 tablespoon of oil to drizzle on vegetables halfway through roasting.

Arrange and Roast

Arrange on sheet pan

Line a large rimmed baking sheet with parchment paper or lightly oil it. Spread the seasoned vegetables in a single layer with some space between pieces — avoid overcrowding to promote even browning. Place potatoes cut-side down for better caramelization.

Roast

Roast in the preheated 425°F (220°C) oven for 20 minutes. After 20 minutes, remove the pan, toss or flip the vegetables for even browning (and drizzle the reserved tablespoon of oil if using). Return to the oven and roast an additional 10–15 minutes, until vegetables are tender and edges are caramelized (total roast time 30–35 minutes depending on your oven and how large you cut the pieces).

Finish and Serve

Rest and finish

Remove the tray from the oven and let the vegetables rest 2–3 minutes. If using, sprinkle 2 tablespoons chopped fresh parsley, 1 tablespoon lemon juice, and 2 tablespoons grated Parmesan over the warm vegetables and gently toss to combine.

Taste and adjust seasoning, adding a pinch more salt or pepper if needed. Serve hot as a side dish or cool to room temperature for use in salads or meal prep.