Pat the pork dry and season both sides with kosher salt and black pepper. Spread ¼ cup of flour on a small plate and lightly dredge the chops; shake off any excess.
Heat a large 12‑inch skillet over medium‑high heat. Add 1 tablespoon olive oil and 1 tablespoon butter. When shimmering and foamy, sear the pork chops for 2½–3 minutes per side until well browned. Transfer to a plate and tent with foil.
Reduce the heat to medium. Add the remaining 1 tablespoon of olive oil, then the mushrooms and a pinch of salt. Cook 6–8 minutes, stirring occasionally, until deeply browned. Stir in the garlic and cook 30–60 seconds until fragrant.
Add the remaining 1 tablespoon of butter and the remaining ¼ cup of flour. Cook for about 1 minute, stirring constantly.
Pour in the Marsala, scraping up the browned bits. Simmer 2–3 minutes to reduce by about half. Stir in the chicken stock and simmer 2–3 minutes until slightly thickened. Stir in the thyme and season with additional salt and pepper to taste.
Nestle the chops (and any accumulated juices) into the sauce. Simmer 2–3 minutes, or until the pork reaches 145°F at the thickest point. Sprinkle with chopped parsley and serve warm.