Heat 1½ tbsp oil in a wide saucepan over high heat, add shallot and stir occasionally until tender (5-10 minutes). Add garlic and cook for 20 seconds, then add cavolo nero, cover with a lid, stir occasionally until wilted and tender (5-7 minutes) and keep warm.
Meanwhile, heat a separate frying pan over high heat, add remaining oil, place fish skin-side down in pan and cook until golden (2-3 minutes), then turn and cook until golden and just cooked through (2-3 minutes). Add butter, capers and rosemary and cook until just crisp (1 minute).
Place cavolo nero on a plate, top with fish, spoon rosemary and capers over, season with sea salt flakes to taste, squeeze over plenty of lemon juice and serve.