First make the butter. Put the wine and shallot into a pan, then bring to the boil and simmer until nearly dry. Tip into a bowl to cool, mix all the ingredients together, roll into a log, using cling film or foil, then chill to harden. Can be frozen for up to 1 month.
Snap away the claws from the lobster. Using a large chef’s knife, cut the lobster in half and wash the head cavity under cold water, then dry with kitchen paper. Lay the lobsters, cut side up, on a baking tray. Crack the claws and remove the claw meat. Divide claw meat between the head cavities. This can be done the day before and the lobster kept in the fridge ready for grilling.
Heat grill to high. Slice the butter into thin rounds and lay it along the lobsters so all the meat is covered. Grill for 5-8 mins until the butter is bubbling and starting to brown. Put the lobsters on plates, pouring any butter from the tray over them. Serve with new potatoes and some dressed salad leaves.