Preheat your oven to 400°F (200°C). Line a large, rimmed baking sheet with parchment paper for easier cleanup.
In a large bowl, combine the sausage pieces, potatoes, broccoli florets, and red onion wedges.
In a small bowl, whisk together the olive oil, minced garlic, rosemary, thyme, salt, pepper, lemon zest, and lemon juice.
Pour the oil mixture over the sausage and vegetables. Toss everything together until evenly coated.
Spread the mixture onto the prepared baking sheet in a single layer. Do not overcrowd the pan; use two pans if necessary to promote roasting instead of steaming.
Roast for 25 to 30 minutes, stirring halfway through, until the potatoes are tender and the sausage is browned and cooked through.
Remove from the oven, sprinkle with fresh parsley, and serve immediately.
Notes
For crispier potatoes, you can boil the potatoes for 5 minutes before tossing them with the oil mixture.
If you prefer a stronger lemon flavor, add a few thin lemon slices to the pan during the last 10 minutes of cooking.
Chicken sausage cooks faster than pork sausage; adjust the cook time based on your sausage type.