01 - Pat chicken breasts completely dry with paper towels. Season both sides generously with kosher salt and freshly ground black pepper.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Sear chicken breasts for 4 to 5 minutes per side until golden brown. Remove from pan and set aside on a plate.
03 - Reduce heat to medium. Add chopped shallots and minced garlic to the same skillet. Sauté for 2 to 3 minutes, stirring frequently, until shallots are softened and fragrant.
04 - Stir in Dijon mustard and whole-grain mustard until well combined. Deglaze the pan with dry white wine, using a wooden spoon to scrape up any browned bits from the bottom. Simmer for 2 minutes to reduce slightly.
05 - Pour in chicken stock and bring to a gentle simmer. Stir in heavy cream and fresh thyme leaves. Continue cooking for 2 minutes until the sauce begins to thicken.
06 - Return chicken breasts along with any accumulated juices to the skillet. Cover and cook for 10 to 12 minutes, until chicken is cooked through (internal temperature reaches 165°F) and sauce has thickened to a creamy consistency.
07 - Taste the sauce and add additional salt or pepper if needed. The sauce should be rich and creamy with a balanced mustard flavor.
08 - Transfer chicken to serving plates. Spoon the mustard cream sauce generously over each portion. Sprinkle with chopped fresh parsley and serve immediately.