Start by cooking the chicken:
Mix the Italian seasoning, salt, pepper and garlic powder together and sprinkle evenly over both sides of the chicken.
Heat a nonstick skillet over medium high heat and add the butter and oil. When the butter has melted and the skillet is hot, add the chicken and sauté until golden brown--about 5-6 minutes per side. Transfer to a plate and cover with foil.
Add the polenta to a medium saucepan, breaking it up with your fingers as you add it. It's okay if there are lumps, they will cook out.
Add the chicken broth, salt, and red pepper flakes if you are using them and stir well.
Bring to a simmer and mash out any lumps, stirring often until the polenta is smooth--about 6 minutes or so. Add the cheese and stir to combine. Turn off the heat and set aside.
Steam the broccoli according the package directions, drain.
Serve by laying 1/2 cup of polenta on a plate, add broccoli and top with sliced chicken. Serve warm.