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, ½ teaspoon salt, ¼ teaspoon pepper, and ½ teaspoon of the Italian seasoning. Spread them out on one side of the baking sheet, making sure they're not overcrowded.
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 vegetables. While the potatoes are getting their head start, in the same bowl, combine the broccoli florets, bell peppers, and red onion. Toss with the remaining 2 tablespoons olive oil, minced garlic, remaining Italian seasoning, smoked paprika, red pepper flakes (if using), ½ teaspoon salt, and ¼ teaspoon black pepper.
Add the vegetables and sausage. After the potatoes have roasted for 10 minutes, remove the pan from the oven. Add the seasoned vegetables to the other side of the baking sheet. Nestle the chicken sausage links among the vegetables.
Roast everything together. 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 heated through with nice browning.
Optional: Broil for perfect finish. For extra caramelization, switch the oven to broil for the last 2-3 minutes, watching carefully to prevent burning.
Rest and serve. Remove from the oven and let rest for a few minutes. Serve hot with lemon wedges for squeezing over the top and fresh herbs sprinkled as garnish if desired.