01 - Pat chicken breasts thoroughly dry with paper towels. Generously season both sides with kosher salt and freshly ground black pepper, pressing seasoning into meat to adhere.
02 - Heat olive oil and butter in a large skillet over medium-high heat until butter foams. Add chicken breasts and sear for 4-5 minutes per side until deeply golden brown. Transfer chicken to a plate and set aside.
03 - Reduce heat to medium. Add chopped shallots to the skillet and sauté for 1 minute until fragrant. Add minced garlic and continue cooking for 1-2 minutes until softened but not browned.
04 - Stir in Dijon mustard and whole-grain mustard, coating the aromatics evenly. Pour in white wine and deglaze the pan, scraping up any browned bits from the bottom with a wooden spoon. Let simmer for 2 minutes until slightly reduced.
05 - Pour in chicken stock and bring to a gentle simmer. Stir in heavy cream and fresh thyme leaves. Cook for 2 minutes until sauce begins to thicken slightly.
06 - Return chicken breasts and any accumulated juices to the skillet. Cover and reduce heat to low. Cook for 10-12 minutes until chicken is cooked through (165°F internal temperature) and sauce has thickened to coat the back of a spoon.
07 - Taste sauce and adjust seasoning with additional salt and pepper if needed. If sauce is too thick, add a splash of chicken stock or water to reach desired consistency.
08 - Transfer chicken to serving plates. Spoon generous amounts of mustard cream sauce over each breast. Sprinkle with freshly chopped parsley and serve immediately.