Preheat the oven to 220°C.
Prick potatoes and bake for 45 minutes until cooked.
Clean scallops, discarding corals and keeping only the main white flesh.
Dry four deep shell halves in the oven for two minutes.
Place shells on a baking tray stabilized by mounds of salt.
Scoop flesh from cooled cooked potatoes and pass through a ricer.
Mix potato with egg yolks and 25g butter until smooth.
Season potato and transfer to a piping bag.
Pan-fry seasoned scallops in butter for about 1 minute per side until brown.
Sauté banana shallot, carrots, leeks, and celery in 75g butter until soft.
Cook sliced shallots in remaining butter, then reduce wine by half.
Add fish stock and reduce by half, then add cream and reduce again.
Stir in champagne, tomatoes, herbs, and lemon juice before removing from heat.
Preheat the grill to a high setting.
Place vegetables and two scallops into each shell and top with sauce.
Pipe potato over the top and sprinkle with Gruyère and breadcrumbs.
Grill for 1 to 2 minutes until the potato is lightly golden.
Serve shells on plates over a mound of salt and dulse seaweed.