Place the chicken breasts between sheets of parchment and gently pound them to an even thickness.
Pat the chicken dry and season both sides with salt and cracked black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken and cook for about 4–5 minutes per side, until golden and cooked through.
Add the butter, garlic, and thyme during the final few minutes of cooking.
Transfer the chicken to a plate and loosely cover with foil.
Reduce the skillet heat to medium and add the minced shallot.
Cook for 1–2 minutes until softened.
Pour in the chicken broth and scrape the browned bits from the bottom of the skillet.
Simmer for 2–3 minutes to reduce slightly.
Lower the heat and stir in the heavy cream, Dijon mustard, Worcestershire sauce, and green peppercorns.
Simmer gently until the sauce thickens enough to coat the back of a spoon.
Taste and adjust the salt if needed.
Return the chicken and any collected juices to the skillet.
Spoon the sauce over the chicken and simmer gently for 1–2 minutes.
Stir in the remaining butter and garnish with fresh parsley.
Serve immediately with mashed potatoes, roasted vegetables, or crusty bread.