Preheat your oven to 425°F (220°C). If your oven has a convection setting, use it for more even browning.
Line a large baking sheet with parchment paper or a silicone mat. This makes cleanup a lot easier.
Toss the sweet potatoes with 1.5 tablespoons of olive oil, a pinch of salt, and half of the minced garlic on a bowl until evenly coated.
Spread the sweet potatoes in a single layer on the sheet pan. Roast for 10 minutes to start caramelizing.
Meanwhile, toss the Brussels sprouts with the remaining 1.5 tablespoons of olive oil, the thyme, paprika, salt, pepper, and the rest of the garlic in another bowl.
Add the sausage links to the sheet pan with the potatoes after the initial 10 minutes. Nestle the Brussels sprouts around the sausage. If you like extra lemon brightness, drizzle a little lemon juice over everything.
Roast for another 15–20 minutes, stirring once or twice, until the potatoes are tender and the sausage is cooked through. The Brussels sprouts should be nicely browned on the edges.
If you prefer crisper Brussels sprouts, flip them midway through roasting and give the sheet another 5–7 minutes. If using a thicker sausage, you may need an extra 5–10 minutes.
Remove from the oven and let rest for a few minutes. Taste and adjust salt if needed. Sprinkle with chopped parsley if you have it.
Serve hot straight from the sheet pan. A squeeze of fresh lemon over the top adds a bright note that cuts through the richness.