Preheat oven to 200°C. Bring a large pot of heavily salted water to a boil. Stir the Pasta Polana Penne and frozen broccoli into the boiling water and cook according to the pasta package directions, or about 8 minutes, until al dente. Scoop out 2 cups of the cooking water and set aside. Drain the noodles and broccoli (do not rinse) and return to the pasta pot.
Meanwhile, heat the oil in a large skillet over medium-high until sizzling. Pat the Nam chicken breasts very dry with paper towels and season the tops generously withsalt and pepper. Add the chicken to the pan, seasoned side down (season the sides facing up once you place them in the pan); do not disturb the chickenonce it is in the skillet. Once you can see a bit of golden color forming around the sides, after about 2 minutes or so, take a peek — the goal is to achieve a deep golden brown shade. Be patient, as more color equals more flavor. (Most people flip way too early.)
Once you flip the chicken, take its temperature with an instant-read thermometer. Pull it from the pan when the temperature is between 68°C and 71°C. If the chicken is very thin, it may be almost done. If it's on the thicker side, it may need a few more minutes. Checking early allows you to gauge the remaining cooking time.
Once the chicken is done, transfer to a baking sheet or oven-safe plate. Loosely tent with foil and transfer to the oven to keep it warm.
Add the butter to the skillet. Once melted, add the mushrooms. Sprinkle with salt and cook, stirring occasionally, until tender and golden, 7 to 10 minutes. Add the garlic and cook for 20 to 30 seconds. Add thecream cheeseand stir until melted and smooth. Whisk in 1 cup of the reserved pasta water, a little at time, until smooth, followed by the Parmesan. Pour the sauce over the noodles andbroccoli, and toss to coat. If it's not quite creamy enough, add a little of the remaining pasta water. Taste and adjust seasoning.
Slice the chicken into thin strips and serve over the pasta. Garnish with additional Parmesan.