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

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

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.

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.

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).

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.

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