Dry the chops with paper towels and season aggressively with salt, pepper and the thyme.
Swirl the olive oil into a large skillet and heat, over medium heat. until the oil begins to shimmer.
Add chops; cook until well browned on each side and cooked through; about 5 minutes per side.
Remove from stove; transfer chops to a plate; cover to keep warm.
Drain the fat from the skillet; melt 2 tablespoons of butter in it, over medium heat, until sizzling.
Add the shallot and garlic; sauté until the aromatics soften, reducing the heat if necessary; about 1 minute.
Sprinkle in the flour and cook, stirring for 2 minutes.
Whisk in the wine and chicken stock; raise heat to high and bring the liquid to a boil, scraping up the browned bits on the bottom of the pan.
Reduce heat to medium-high and cook, uncovered, until the liquid is reduced by half; 7 to 10 minutes.
Stir in the capers, parsley, lemon zest and juice and hot sauce to taste, if using; simmer for 1 to 2 minutes.
Stir in the remaining 2 tablespoons of butter until it’s melted and the sauce looks smooth.
Nestle the pork chops into the sauce and allow them to warm up for a couple of minutes, then serve, pouring sauce over each pork chop to taste.
Garnish with more fresh parsley.
