Preheat the oven to 425°F (220°C).
In a large bowl, combine the sweet potato cubes with 1 tablespoon of olive oil, 1/2 teaspoon of garlic powder, 1/2 teaspoon of smoked paprika, 1/4 teaspoon of salt, and 1/8 teaspoon of black pepper. Toss until the sweet potatoes are evenly coated.
Spread the sweet potatoes in a single layer on a large sheet pan. Roast in the preheated oven for 15 minutes.
While the sweet potatoes roast, in the same large bowl, combine the broccoli florets with the remaining 1 tablespoon of olive oil, 1/2 teaspoon of garlic powder, 1/2 teaspoon of smoked paprika, 1/4 teaspoon of salt, and 1/8 teaspoon of black pepper. Toss to coat evenly.
After the sweet potatoes have roasted for 15 minutes, remove the sheet pan from the oven. Add the sliced sausage and the seasoned broccoli florets to the pan, spreading everything out in an even layer.
Return the sheet pan to the oven and roast for an additional 15 minutes, or until the broccoli is tender and slightly browned, the sweet potatoes are cooked through, and the sausage is heated.
Remove from the oven and let cool for 3-5 minutes before serving.