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 4–5 minutes per side until deep golden brown. Transfer to plate and rest.
03 - Reduce heat to medium. Add chopped shallots to rendered drippings; sauté 2–3 minutes until translucent. Add minced garlic and cook 30 seconds until fragrant.
04 - Stir in Dijon and whole-grain mustards, coating aromatics evenly. Pour in white wine, scraping browned fond from pan bottom. Simmer 2 minutes until slightly reduced.
05 - Add chicken stock and bring to gentle simmer. Pour in heavy cream and sprinkle fresh thyme leaves. Stir to incorporate fully.
06 - Return seared chicken to skillet, nestling into sauce. Cover and cook 10–12 minutes over medium-low heat until chicken reaches internal temperature of 165°F and sauce thickens to coat spoon.
07 - Taste sauce and adjust salt or pepper as needed. Sauce should balance creaminess with mustard sharpness.
08 - Transfer chicken to serving plates. Spoon generous amount of mustard sauce over each portion. Sprinkle with chopped fresh parsley and serve immediately.