Season the chicken with salt and pepper. In a Dutch oven or straight-sided skillet with a lid, sauté the chicken in butter over medium heat, just until the chicken is brown on both sides. You don't need to cook the chicken pieces through. Using a slotted spoon or tongs, remove from the pan and set aside.
Add a little of the chicken stock and scrape the brown bits off the bottom of the pan. Add the rest of the stock and the cream and bring to a simmer. Add garlic powder, onion powder, rosemary, chicken and pasta. Turn the heat to low and put the lid on the pot. Cook for 15 or 20 minutes, stirring a couple of times.
When the pasta is done--you'll test it by biting a piece--turn off the heat and add the parmesan and the lemon zest and juice. Season to taste with salt and pepper. If the lemon is too sour, you can add a dash of honey to tame it. Serve immediately with extra parmesan.