Preheat the oven to 350°F.
Add the broccoli to a large bowl. Drizzle with half the olive oil, season with salt and pepper, and toss to coat. Spread into a 9x13-inch baking dish and roast for 10 minutes.
While the broccoli roasts slice the kielbasa into bite-sized pieces. Add the kielbasa and tortellini to the same bowl. Add the minced garlic and remaining olive oil and toss until everything is well coated.
Remove the baking dish from the oven. Add the kielbasa and tortellini mixture to the dish with the broccoli. Pour the broth evenly over everything.
Cover tightly with foil and bake for 20 minutes until the tortellini is tender and everything is heated through.
Remove from the oven and top with grated Parmesan. Serve warm.