Preheat your oven to 425°F.
Combine the broccoli florets, minced garlic, smoked sausage slices, and two teaspoons of the chopped herbs in a large rimmed baking sheet. Drizzle with olive oil, sprinkle kosher salt and freshly ground black pepper, then mix well to coat everything.
Arrange the mixture evenly across the pan and roast in the oven until the broccoli starts to develop a golden color, about 20 minutes.
Next, add the chopped bell peppers to the pan, stir them in gently, and spread the ingredients out evenly again.
Place the pan back in the oven and continue roasting until the sausage is nicely browned and all the vegetables are tender, which should take another 15 to 20 minutes.
When ready, sprinkle the remaining teaspoon of herbs over the dish and add grated Parmesan cheese, if desired, before serving.