Mince the leaves of 2 sprigs oregano. Combine with the breadcrumbs and paprika. Place the pork chops between two pieces of waxed or parchment paper and bash with a rolling pin or heavy skillet until they are about ¼-inch thick. Season both sides of the pork chops generously with salt and pepper and sprinkle with garlic powder. Press the breadcrumbs onto both sides then bash again to really press them into the pork and make sure they stick.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add the butter and let melt. Add the pork chops and cook about 3 minutes per side or until golden brown. Remove from pan.
Add the remaining ½ tablespoon of oil to the pan, add the tomatoes and pull the leaves off the remaining sprigs of oregano and add to the tomatoes along with the vinegar. Season with a generous pinch of salt and pepper. Cook, tossing for 1 minute. Spoon on top of the pork chops and top with the feta.