Heat your oven to 425°F and line a large baking sheet with parchment or foil. This keeps the food from sticking and makes cleanup easy. Set the pan aside while you chop the ingredients.
Whisk the olive oil, balsamic vinegar, garlic powder, and black pepper in a small bowl. This simple mixture flavors every vegetable on the pan. Save some of it for the broccoli later.
Peel the sweet potatoes and cut them into medium cubes of about one inch. Slice the sausage into bite-sized pieces. Try to keep everything close to the same size so it cooks at the same pace.
Toss the sweet potato cubes with part of the oil mixture, then spread them in a single layer on the pan. Roast them for 15 minutes. They need this head start because they take the longest to soften.
After 15 minutes, pull the pan from the oven and add the sausage pieces. Give everything a quick stir so the sausage touches the hot pan. Return it to the oven and roast for 10 more minutes.
While the pan roasts, cut the broccoli into pieces about the size of the other ingredients. Put it in the bowl and toss it with the remaining oil mixture. Every floret should have a light, shiny coating.
Take the pan out and flip the sausage pieces. Tuck the broccoli in between the sausage and sweet potatoes. Roast for 15 more minutes, until the broccoli is done the way you like it and the sausage and potatoes are nicely browned.
Taste the dish and add salt and fresh black pepper if it needs them. Serve it right away while everything is hot and crisp. It is a complete meal on one pan.