Preheat the oven to 425°F (220°C).
In a large bowl, combine the sliced smoked sausage, red bell pepper pieces, yellow bell pepper pieces, red onion pieces, and broccoli florets.
Drizzle 2 tablespoons of olive oil over the sausage and vegetables. Add smoked paprika, garlic powder, onion powder, crushed red pepper flakes, salt, and black pepper. Toss everything together until evenly coated.
Spread the sausage and vegetable mixture evenly on a large rimmed baking sheet.
Roast in the preheated oven for 12 minutes.
While the sausage and vegetables begin roasting, place the peeled and deveined shrimp in the same large bowl used earlier.
Add the remaining 1 tablespoon of olive oil, a pinch of salt, and black pepper to the shrimp. Toss to coat.
After the initial 12 minutes of roasting, remove the baking sheet from the oven and add the shrimp evenly over the sausage and vegetables.
Return the baking sheet to the oven and roast for an additional 8 minutes, or until the shrimp are pink and opaque and the vegetables are tender.
Remove the sheet pan from the oven and sprinkle the chopped fresh parsley over the top.
Serve immediately.