Heat the oven: Preheat to 425°F (220°C). Place a large rimmed sheet pan inside while it heats.
A hot pan helps everything brown better.
Prep the sausage: If using smoked or fully cooked sausage, slice into 1/2-inch coins on a bias. If using fresh Italian sausage, cut into 2-inch pieces or leave as links. Pat dry for better browning.
Cut the veggies: Keep pieces similar in size.
Halve small potatoes; slice peppers and carrots; cut onion into wedges; break broccoli into medium florets. Dry any wet surfaces with a towel.
Season: In a large bowl, toss veggies with olive oil, garlic, Italian seasoning, smoked paprika, thyme, salt, and pepper. Use enough oil to lightly coat—about 3 tablespoons for a full pan.
Load the pan: Carefully remove the hot sheet pan.
Spread the vegetables in an even layer with some space between pieces. Nestle sausage throughout.
Roast, then toss: Roast for 15 minutes. Stir and flip everything to expose new surfaces.
Rotate the pan if your oven has hot spots.
Finish roasting: Cook 10 to 15 minutes more until the sausage is browned and the vegetables are tender with crisp edges. Potatoes should be easily pierced with a fork.
Add brightness: Squeeze lemon over the pan or drizzle with balsamic. Taste and adjust salt, pepper, or acid.
Serve: Top with chopped parsley.
Pair with crusty bread, steamed rice, quinoa, or a simple green salad.