Preheat the oven to 200C/400F/Gas 6.
Open the oysters carefully, retaining the juice. Cover the oysters with a clean cloth, but do not refrigerate.
Melt the butter in a pan and add the shallot. Cook gently without colouring.
Add the vermouth, oyster juice and stocks. Cook until the volume of liquid has reduced by two thirds.
Add the cream and cook until the volume has reduced by half.
Shuck the oysters, pry them from the shells and set aside. Clean the deeper shells and lay them on a tray, then put a little of the sauce in the base of each shell. Lay an oyster in each shell and transfer to the oven for two minutes. Preheat the grill to hot.
Stir the mustard into the remaining sauce. Remove the sauce from the heat and stir in the egg yolks, followed by the parsley and half of the parmesan.
Take the oysters out of the oven and pour a little sauce over each one. Sprinkle the remaining parmesan over the top.
Cook the samphire in a pan of boiling salted water for 1-2 minutes, or until tender. Drain well.
Meanwhile grill the oysters to glaze them. Serve with the samphire.