Step 1

Preheat oven to 300 degrees F (150 degrees C).

Step 2

Pound pork chops between 2 sheets waxed paper or plastic wrap until very thin, about 1/8 inch.

Step 3

Mix flour, salt, and pepper together in a shallow bowl. Dredge both sides of each pork chop through flour mixture, shaking off any excess flour.

Step 4

Heat butter in a large skillet over medium heat until butter starts to sizzle. Add shallots and pork chops in 1 layer, working in batches if needed. Cook pork chops until golden brown and almost cooked through, 3 to 4 minutes per side. Transfer pork chops to a baking dish and lightly tent with aluminum foil, reserving the shallots and browned bits of food in the skillet.

Step 5

Bake pork chops in the preheated oven until cooked through, 20 to 25 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).

Step 6

Pour wine and chicken stock into the skillet and bring to a boil while scraping the browned bits of food off of the bottom with a wooden spoon. Reduce heat and simmer until sauce is reduced by half, 2 to 5 minutes. Stir lemon juice into sauce.

Step 7

Drizzle sauce over pork chops and top with parsley, lemon zest, and capers.