Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
On a large rimmed sheet pan, combine the refrigerated tortellini, broccoli florets, and cubed chicken breast.
Drizzle olive oil over the ingredients and sprinkle with minced garlic, salt, pepper, and red pepper flakes.
Toss all ingredients directly on the pan until evenly coated, then spread into a single layer.
Roast for 18 to 20 minutes, or until the broccoli is tender and the tortellini are heated through with slightly golden edges.
Remove from oven and immediately sprinkle with grated parmesan cheese before serving.