Pat the chicken thighs dry. Season with the kosher salt and freshly ground black pepper.
Heat the olive oil and butter in a large skillet over medium-high heat. Add the chicken and cook for 5–6 minutes on the first side, until deeply golden. Flip and cook for another 4–5 minutes, or until the chicken reaches 165°F. Transfer to a plate.
Reduce the heat to medium. Add the butter and shallots to the same skillet. Cook until the shallots soften. Add the coarsely crushed peppercorns and cook briefly, until fragrant.
Carefully pour in the brandy or Cognac and stir, scraping up the browned bits from the bottom of the skillet. Let it cook briefly to reduce.
Add the chicken broth and bring to a simmer. Cook for 3–5 minutes, allowing it to reduce.
Stir in the heavy cream and mustard. Simmer for another 3–5 minutes, until the sauce has thickened enough to lightly coat the back of a spoon.
Return the chicken and any accumulated juices to the skillet. Spoon the sauce over the chicken and let everything cook together for 1–2 minutes.
Finish with fresh parsley and serve over creamy mashed potatoes.