Melt 2 tablespoons butter in a large skillet over medium heat. Add the apples, onion, caraway seeds, 1/4 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the apples start browning around the edges, about 4 minutes. Add the sauerkraut and cook until the excess liquid evaporates, about 2 minutes. Add the apple cider and chicken stock and bring to a simmer. Reduce the heat to medium low and cook until the apples and onion soften, about 8 minutes.
Meanwhile, season the pork with the paprika, 1 teaspoon salt and a few grinds of pepper. Melt the remaining 2 tablespoons butter in a separate large skillet over medium heat. Working in two batches, cook the pork until browned and just cooked through, 1 to 2 minutes per side. Transfer to a plate. Serve the pork with the sauerkraut mixture; top with the parsley.