Bring a large of salted water to the boil and then reduce to medium heat.
Cook the lobster for 14 minutes.
If preparing the dish in advance, immediately place the cooked lobster in a bowl of iced water and refrigerate until needed.
To serve, melt the butter in a pot over a medium heat.
Take a medium-sized bowl and combine the yolks and whole egg and whisk.
Prepare a bain-marie using the bowl containing the whisked eggs.
Whisk the eggs while cooking and ensure they double in volume.
Once doubled, remove from the heat and slowly whisk the melted butter into the egg mixture.
Season with salt and cracked pepper to taste.
If preparing in advance, reserve in a bowl and cover with clingfilm.
To serve, cut the lobster in half and pour over the sauce on the meat, serve with the brioche roll warmed in the oven.