Season the chicken. Sprinkle both sides of the chicken with the salt, pepper, and garlic powder. Pat the spices in so they adhere.
Sear until golden. Heat the olive oil in a large skillet over medium-high heat.
Add the chicken and cook 4–6 minutes per side, until deep golden and nearly cooked through. Transfer to a plate; tent loosely with foil.
Sauté aromatics. Reduce heat to medium. Add the butter to the skillet.
Stir in the garlic and shallot, cooking 30–60 seconds until fragrant. Don’t let the garlic brown.
Deglaze the pan. Pour in the wine (or 1/2 cup broth). Scrape up browned bits with a wooden spoon.
Simmer 1–2 minutes to reduce slightly.
Build the sauce. Add the remaining 1 cup broth, Dijon, whole-grain mustard (if using), and thyme. Whisk until smooth. Simmer 3–4 minutes to let it thicken a touch.
Add the cream. Lower the heat and stir in the cream.
Simmer gently 2–3 minutes. Taste and adjust salt and pepper. The sauce should coat a spoon.
Finish the chicken. Return the chicken to the skillet and spoon sauce over the pieces.
Simmer 2–4 minutes, until the chicken is cooked through and the sauce is silky.
Brighten and garnish. Stir in the lemon juice to lift the flavors. Sprinkle with parsley. Serve hot with your favorite sides.