For the carrots, make a layer of sea salt about 3cm thick in a roasting tin. Place the carrots on top and bake for 20–30 minutes until they are tender. Remove from the oven and scrape off the skins using a tea towel. Cut each carrot in half lengthways and then into 3–5cm-long pieces.
Clean the herrings and cut off the fins and head. Butterfly each herring by removing the backbone but keeping the fillets attached to the skin in one piece. Season with a pinch of salt on each side. Set aside for 30 minutes.
Clean and rinse the clams in cold water. Drain. Heat a wide pan over a high heat. Add the clams, cover with a lid and steam for 3–4 minutes, stirring regularly, until all the clams are open. Remove from the heat and add the butter. Stir until the butter has melted, then add the vinegar. Strain the liquid into another pan and set aside. Reserve the clams.
Place each butterflied herring, skin side down, on a burning log to smoke for 3 minutes. Flip the herrings over and smoke for a further 1 minute. Meanwhile, heat the carrots and clams in the buttery clam jus. To serve, top the herrings with the clams, carrots and jus.