01 - Pat chicken breasts dry with paper towels and 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. Add chicken breasts and sear for 4–5 minutes per side until golden brown and caramelized. Transfer chicken to a plate and set aside.
03 - Reduce heat to medium. Add chopped shallots and minced garlic to the skillet; sauté for 2–3 minutes until softened and fragrant, being careful not to burn the garlic.
04 - Stir in Dijon mustard and whole-grain mustard until evenly distributed. Deglaze the pan with white wine, using a wooden spoon to scrape up the browned bits from the bottom. Let 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. Allow the sauce to cook for 1–2 minutes until slightly thickened.
06 - Return chicken breasts to the skillet, nestling them into the sauce. Cover and cook for 10–12 minutes until chicken is cooked through (internal temperature reaches 165°F) and sauce has thickened to a creamy consistency.
07 - Taste the sauce and adjust salt and pepper as needed. If sauce is too thick, add a splash of chicken stock; if too thin, continue simmering uncovered for a few minutes.
08 - Transfer chicken to serving plates and spoon the mustard sauce generously over the top. Sprinkle with chopped fresh parsley and serve immediately.