In a large pot, cook pasta according to package instructions for al dente. Add broccoli to the pasta in the last three minutes of cooking. Drain and return to the pan. Add chopped dried tomatoes.
In a large skillet or frying pan, melt butter over medium heat.
Add chicken, onions, seasonings, and red pepper flakes to the pan and cook until the chicken is thoroughly cooked and onions are tender.
Sprinkle flour over the chicken mixture, stir, and cook for an additional 1-2 minutes.
Pour milk and chicken broth into the skillet, stir, and bring to a boil over medium heat.
Once the sauce has thickened slightly, add cheese and stir until combined.
Pour the sauce mixture into the pasta and broccoli. Stir to combine.
Serve warm, optionally accompanied by a side salad or crusty bread with butter or garlic bread.