Prep the chicken: Pat chicken dry.
Season both sides with salt and pepper. If breasts are thick, slice horizontally to create cutlets for faster, more even cooking.
Sear the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken and cook 4–5 minutes per side until golden and cooked through (165°F).
Transfer to a plate and tent with foil.
Sauté the mushrooms: Reduce heat to medium. Add butter to the same skillet. Stir in mushrooms and a pinch of salt.
Cook 6–8 minutes, stirring occasionally, until browned and most liquid has evaporated.
Add aromatics: Stir in onion and cook 2–3 minutes until softened. Add garlic and thyme; cook 30 seconds until fragrant.
Build the sauce: Sprinkle flour over the mushrooms and stir for 30 seconds to coat. Pour in chicken stock while stirring, scraping up browned bits.
Simmer 2–3 minutes until slightly thickened.
Make it creamy: Lower heat to medium-low. Stir in heavy cream and Dijon. Simmer gently 2 minutes until the sauce is silky.
Taste and adjust salt and pepper.
Return the chicken: Nestle chicken back into the skillet, along with any juices from the plate. Spoon sauce over the top.
Top with Swiss: Lay Swiss cheese slices over the chicken. Cover the skillet and cook 2–3 minutes, just until the cheese melts and the chicken is heated through.
Finish and serve: Garnish with parsley.
Serve over mashed potatoes, egg noodles, rice, or with crusty bread to soak up the sauce.