Preheat the oven and prep the pan: Set your oven to 425°F (220°C).
Line a large sheet pan with parchment paper or lightly oil it for easier cleanup.
Prep the vegetables: Cut potatoes into 1-inch chunks for faster roasting. Slice bell peppers and onion into sturdy pieces so they don’t burn. Trim broccoli into medium florets or halve Brussels sprouts for even cooking.
Season the vegetables: In a large bowl, toss potatoes, peppers, onion, and broccoli with 2 tablespoons olive oil, garlic, smoked paprika, Italian seasoning, thyme, salt, and pepper.
Make sure everything is evenly coated.
Start the roast: Spread the vegetables in a single layer on the sheet pan. Roast for 15 minutes to give the potatoes a head start.
Slice and add the sausage: While the veggies start roasting, slice the sausage into 1/2-inch rounds. If using uncooked sausage links, keep them whole for now.
Add sausage to the pan: After 15 minutes, remove the pan, toss the veggies, and add sausage rounds on top.
If using uncooked links, nestle whole links among the vegetables. Drizzle with the remaining 1 tablespoon olive oil if things look dry.
Finish roasting: Return to the oven for 18–22 minutes, until the potatoes are tender and the sausage is browned and sizzling. If using uncooked links, roast until an instant-read thermometer reads 160°F (71°C), then slice if desired.
Optional broil: For extra char and crisp edges, broil for 2–3 minutes at the end.
Watch closely to avoid burning.
Finish and serve: Squeeze fresh lemon over the pan for brightness and toss gently. Sprinkle with chopped parsley or dill. Taste and adjust salt or pepper.
Serve hot.