Prepare the chicken: Pat the chicken breasts very dry with paper towels (dry surface = better sear). Season both sides with 1 tsp kosher salt and 1/4 tsp black pepper. Lightly dredge both sides in 2 tbsp flour and shake off excess (the thin flour coating helps develop a golden crust and gives the sauce a little body when the pan deglazes). Let rest 5–10 minutes at room temperature while you prep aromatics.

Heat the pan and sear the chicken: Heat a large stainless-steel or cast-iron skillet over medium-high heat until hot. Add 1 tbsp olive oil and 1 tbsp butter — this combination gives a high smoke point plus the butter's flavor. When the butter foams, add the chicken. Sear without moving 4–5 minutes per side until deeply golden (internal temp ~150°F/65°C since it will finish in the sauce). A good sear creates fond (browned bits) that form the flavor base for the pan sauce.

Remove chicken and rest: Transfer the browned chicken to a plate and tent loosely with foil. Resting preserves juices and prevents the sauce from overcooking the meat while you build flavor in the pan.

Sauté aromatics and mushrooms: Reduce heat to medium. Add remaining 1 tbsp butter to the hot pan. Add the chopped onion and sauté 3–4 minutes until translucent — this mellows the onion and releases natural sugars. Add sliced mushrooms and a pinch of salt; cook until mushrooms release moisture and begin to brown (4–5 minutes). Stir in minced garlic and cook 30–45 seconds until fragrant — avoid browning the garlic to keep it from turning bitter.

Deglaze the pan with white wine: Pour in 1/2 cup dry white wine and use a wooden spoon to scrape up the browned bits (fond) from the bottom of the pan — that flavor is the backbone of the sauce. Let the wine reduce by about half (2–3 minutes) so alcohol cooks off and the flavor concentrates.

Add stock and simmer: Stir in 1 1/4 cups chicken stock and 1 tsp fresh thyme. Bring to a simmer and reduce by about 25% (3–4 minutes). Reducing concentrates flavor and ensures the sauce won’t be watery when you add the cream.

Finish the sauce with cream and mustard: Lower heat to medium-low and stir in 1 cup heavy cream and 1 tbsp Dijon mustard. Whisk gently to combine; heat just until the sauce simmers gently — vigorous boiling can break the emulsion and make the sauce separate. Taste and season with remaining 1/2 tsp kosher salt, 1/4 tsp black pepper and crushed red pepper if using.

Return chicken to the pan to finish cooking: Nestle the seared chicken into the sauce and spoon some sauce over the breasts. Simmer gently 5–6 minutes, flipping once, until internal temperature reaches 160–165°F (71–74°C) and sauce has thickened slightly. Finishing in the sauce keeps the chicken succulent and allows the flavors to meld.

Adjust thickness and acidity: If you prefer a slightly thicker sauce, whisk 1 tsp cornstarch with 1 tbsp cold water and stir into simmering sauce; cook 1–2 minutes more until glossy. Stir in 1 tbsp lemon juice to brighten the sauce and cut the richness — acid lifts cream sauces and balances the palate.

Finish and serve: Remove pan from heat. Stir in 2 tbsp chopped parsley for freshness. Taste and adjust seasoning. Serve the chicken hot with plenty of sauce spooned over. Suggested accompaniments: mashed potatoes, buttered egg noodles, rice or crusty bread to soak up the sauce.