Preheat the oven to 500˚. Place the cabbage on a baking sheet, leaving room for the pork. Brush the cabbage all over with the melted butter; season with salt and pepper. Roast 15 minutes.
Meanwhile, rub the pork with salt, pepper and the coriander. Melt 1 tablespoon butter in a large skillet over medium-high heat. Add the pork and cook, turning, until browned all over, 8 minutes (reduce the heat if the pork is getting too dark). Transfer the pork to the baking sheet with the cabbage; reserve the skillet. Roast the pork and cabbage together until a thermometer inserted in the center of the pork registers 145˚, 13 to 15 minutes; transfer to a cutting board. Continue roasting the cabbage until browned, 5 to 10 more minutes.
Melt the remaining 1 tablespoon butter in the reserved skillet over medium-high heat. Add the bell pepper, onion and garlic and season with salt and pepper. Cook, stirring occasionally, until the onion is soft, about 5 minutes. Add the paprika and stir until toasted, 30 seconds. Stir in the vinegar and sugar, then pour in 1/3 cup water, scraping up the bottom of the skillet. Cook until a thin sauce forms, 1 to 2 minutes; season with salt and pepper.
Slice the pork and divide among plates along with the cabbage. Spoon the bell pepper mixture over the pork; top with the parsley.