Wash cuttlefish under cold running water (defrost if necessary). Separate heads from bodies with a sharp knife, then remove tentacles and set aside, discarding the eyes and beaks with the hard parts around them. Pull out hard "bone" from bodies and discard. Cut bodies lengthwise to open, carefully avoiding piercing the small, silvery ink sacs. Detach sacs, and set aside. Remove and discard entrails. Peel off thin outer skin under cold running water, if you like. Slice cuttlefish and tentacles into medium-size pieces. Rinse under cold water and set aside to drain.
Heat oil and butter in a large pan with lid over medium heat. Add onions and cook, stirring often, until soft, about 10 minutes. Add cuttlefish and reserved tentacles and cook until heated through, then add wine and cook until alcohol has evaporated, 3–5 minutes.
Mix together tomato paste and 1 cup water in a small bowl, then add to cuttlefish along with ink sacs (or 2–3 tbsp. cuttlefish ink) and half the chopped parsley. Stir to mix, pressing on ink sacs with the back of a wooden spoon to break the skin and release the black ink within. (Some sacs may already have broken, losing some of their liquid and leaving a thick ink paste behind.) Reduce heat to medium-low, cover, and cook, stirring occasionally, until cuttlefish is very tender, 40–60 minutes. Uncover pan for the last 10 minutes of cooking to reduce and thicken sauce slightly. Sprinkle with remaining chopped parsley and serve with white or (yellow) polenta, if you like.