01 - Pat chicken breasts completely dry with paper towels, then 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 and sear for 4-5 minutes per side until golden brown. 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 well combined. 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 to reduce slightly.
05 - Pour in chicken stock and bring to a gentle simmer. Add heavy cream and fresh thyme leaves, stirring to incorporate. Let the sauce cook for 1-2 minutes until slightly thickened.
06 - Return chicken breasts along with any accumulated juices to the skillet. Cover and cook for 10-12 minutes until chicken is cooked through (internal temperature reaches 165°F) and sauce has thickened to coat the back of a spoon.
07 - Taste the sauce and adjust seasoning with additional salt and pepper if needed. If sauce is too thick, add a splash more chicken stock to reach desired consistency.
08 - Transfer chicken to serving plates or a platter. Spoon the creamy mustard sauce generously over the top. Garnish with chopped fresh parsley and serve immediately.