Cut the chicken into 1-inch, bite-size pieces and chop all the vegetables.
Set a large cast iron skillet (or sauté pan) over medium heat. Add the butter, mushrooms, and onions. Sauté the mushrooms, stirring occasionally, until they release their moisture and dry out again. They should start to caramelize around the edges, 5-8 minutes.
Push the mushrooms and onions to the sides of the pan and add in the chicken. Salt and pepper generously, and cook for 3 minutes, stirring once or twice.
Add in the bell peppers, thyme, paprika, and nutmeg. Stir and cook another 2 minutes. Then mix in the cream cheese, chicken broth, sherry, and peas. Stir and simmer until the cream cheese melts into the liquid creating a smooth sauce. (If you use nonfat cream cheese, you may need to whisk it a bit so it incorporates into the sauce.)
Turn off the heat. Stir in the parsley and lemon juice. Then taste, and salt and pepper as needed. Serve immediately.
NOTES: Chicken A La King is traditionally served with toasted bread or with puff pastry. This lean version skips the extra carbs, but you could certainly add them back in. Also, this dish does not make a great leftover. Eat it up the first day.