01 - Season both sides of the chicken breasts evenly with salt and black pepper.
02 - Heat olive oil in a large skillet over medium-high heat, add chicken and cook 5 to 6 minutes per side until golden and cooked through. Remove and keep warm covered loosely with foil.
03 - Reduce heat to medium, add butter to the skillet, sauté onions for 2 minutes, then add garlic and mushrooms; cook until mushrooms are golden and moisture evaporates, about 5 to 7 minutes.
04 - Pour in chicken broth, scraping browned bits from the pan, and simmer for 2 minutes.
05 - Add heavy cream, Dijon mustard, and thyme; stir and simmer gently for 2 to 3 minutes until sauce slightly thickens.
06 - Stir in grated Parmesan until melted and sauce becomes creamy.
07 - Return chicken and accumulated juices to the skillet; simmer 2 to 3 minutes until heated through and well coated with sauce.
08 - Sprinkle fresh parsley over the dish and serve immediately.