Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions. About 3 minutes before the pasta is done, add the broccoli florets directly into the pot.

In a large skillet, heat the olive oil over medium heat. Add the diced onions and cook until translucent. Follow with the minced garlic, being careful not to let it burn.

Add the shredded chicken to the skillet. Cook until warmed through. Sprinkle in the red pepper flakes if using.

Using a slotted spoon or tongs, transfer the pasta and broccoli directly from the water into the skillet. Add a splash of pasta water to the pan to help create a light sauce. Remove the pan from the heat and stir in the grated parmesan cheese.

Season with salt and black pepper. Toss everything together until well combined and the cheese is melted.