Place the lemon pepper marinate ingredients into a large zip-style bag. Squish gently around with your fingers to combine the ingredients. Fold the top of the bag over, so you can easily place the flattened chicken breasts in.
In a zip-style large bag pound the chicken breasts, one at a time to flatten. Use a rolling pin or meat tenderizer. (keep one hand clean- one hand touching chicken) You want to rotate your rolling pin, back and forth in different directions, so that you evenly flatten out the chicken. Place flattened chicken breasts into the marinate bag. Let sit in the refrigerator for 4 hours minimum. The more they sit and marinate, the more flavorful and moist they will become.
Grill the chicken on high heat, about 5 to 6 minutes each side. Place on a plate, cover with aluminum foil to keep warm and let the juices rest.
In a large cast iron skillet or pan, heat 2 tablespoons olive oil and 1 tablespoon of butter over medium heat. Add the diced onion and saute until translucent, about 8 minutes. Occasionally stir the onions with a wooden spoon to prevent them from burning. Add the sliced mushrooms and brown. Continue to stir with a wooden spoon occasionally.
De-glaze the pan by adding the chicken stock and scraping the browned on goodness with a wooden spoon. Add the Greek cream cheese and stir to dissolve and incorporate. Add the frozen carrots and broccoli florets and cook for about 7 or 8 minutes. Add the packets of Uncle Ben's Ready Rice and stir to combine. Let cook an additional 5 to 6 minutes until thoroughly heated. Cover to keep warm until served.
Serve with the grilled chicken and enjoy.