01 - Season both sides of the chicken breasts with salt and black pepper.
02 - Heat olive oil in a large skillet over medium-high heat. Add chicken breasts and cook until golden brown on both sides, about 4 to 5 minutes per side. Transfer to a plate and set aside.
03 - In the same skillet, sauté the chopped onion for 2 to 3 minutes until softened. Add garlic and mushrooms, cooking until mushrooms are browned and moisture has evaporated, approximately 5 minutes.
04 - Pour in the gluten-free chicken broth, scraping up browned bits from the skillet bottom. Stir in heavy cream, thyme, Dijon mustard, and Parmesan cheese if using.
05 - Return the chicken breasts to the skillet, cover, and simmer over low heat for 10 to 12 minutes until cooked through and the sauce thickens.
06 - Remove from heat and sprinkle with chopped fresh parsley. Serve immediately with rice, pasta, or crusty bread.