Sprinkle the chicken pieces on both sides with half of the salt and half of the pepper. Heat olive oil to medium in a 10 inch skillet. Brown the chicken for about 4 minutes per side. Set aside.
In the same skillet, brown the sliced mushrooms. Set aside.
Reduce heat to low. Melt the butter and stir in the pressed garlic. Whisk in the flour and cook for 2 minutes until bubbly, stirring constantly. Whisk in the cream and broth until smooth. Stir in the remaining salt, pepper, and parmesan cheese.
Cook on low, stirring until the cheese is melted. Add spinach, peppers, chicken and mushrooms. Stir and heat through. Serve over pasta if desired.