Preheat your oven to 425°F (220°C). Line a large rimmed baking sheet with parchment paper or foil for easier cleanup.
Start with the potatoes. In a large bowl, toss the halved baby potatoes with 1 tablespoon olive oil, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon of the Italian seasoning. Spread them out on one side of the baking sheet.
Give the potatoes a head start. Place the sheet pan with just the potatoes in the oven and roast for 10 minutes. Potatoes take longer to cook than the other ingredients, so this ensures everything will be perfectly done at the same time.
Prep the remaining ingredients. While the potatoes are getting their head start, in the same bowl, combine the sliced sausage, bell peppers, zucchini, yellow squash, and red onion. Toss with the remaining 2 tablespoons olive oil, minced garlic, remaining Italian seasoning, smoked paprika, and red pepper flakes (if using).
Add everything to the sheet pan. After the potatoes have roasted for 10 minutes, remove the pan from the oven. Add the sausage and vegetable mixture to the other side of the baking sheet, spreading everything out in a single layer as much as possible.
Roast to perfection. Return the pan to the oven and roast for an additional 15-20 minutes, or until the potatoes are tender, the vegetables are caramelized around the edges, and the sausage is browned.
Optional: Broil finish. For extra caramelization, switch the oven to broil for the last 2-3 minutes, watching carefully to prevent burning.
Serve and garnish. Remove from the oven and sprinkle with fresh chopped parsley. Serve hot with lemon wedges on the side if desired.