Place the cauliflower for the purée in a small pan and cover with half milk and half water. Season with salt and cook until completely tender. Transfer to a blender and blitz with the butter and enough of the cooking liquid to make a silky purée. Season to taste.
Season the fish with salt and wrap tightly in clingfilm to cure for 30 minutes. Rinse off and dry thoroughly. Heat the olive oil in a pan and add the Norwegian haddock loins. Seal all over, then add the butter and baste. Finish cooking in a hot oven for 2-3 minutes until just cooked through. Drain on paper towel and allow to rest for a couple of minutes.
While the fish is cooking, heat the butter for the brown butter in a small stainless steel pan until it is fragrant and the solids have turned a light brown colour. Add a squeeze of lemon juice to stop the cooking. Add the capers, sultanas and parsley and adjust the seasoning with salt and pepper.
Place the rösti rectangles to one side of the plates and lay the fish on top. Spoon some purée onto the plates and scatter the cauliflower florets around. Dress with the brown butter.