Bring a large pot of water to a boil over high heat. Salt generously and cook the pasta according to package directions. Drain the pasta, reserving a cup of the starchy cooking water.

While the pasta is cooking, heat olive oil in a large skillet over medium-high heat. Season the chicken with salt and pepper and add it to the hot pan. Cook the chicken, stirring occasionally, until golden brown and cooked through 7-10 minutes.

While the chicken is cooking, place about one inch of water in a medium size pot with a steamer basket. Bring to a boil over medium-high heat. Add the broccoli, cover, and reduce heat to medium low. Let cook until broccoli reaches desired tenderness, 2-5 minutes. Remove from the pot and add to the pan with the chicken, tossing to combine.

Return the empty pasta pot to the stove top and melt the butter over medium heat. Add the Parmesan cheese and pasta and toss to coat, adding some of the reserved pasta water as needed to loosen it up.

Serve the pasta by twirling it into a nest and placing the chicken and broccoli in the middle. Top with additional Parmesan and crushed red pepper flakes, if desired.