Preheat oven (electric cooker: 80°C/ circulating air and gas: not suitable). Pat the steak dry. Heat the oil in an ovenproof pan. Brown the steak for 2 minutes on each side. Season with salt and pepper. Bake in the oven for approx. 2 hours.
For the béarnaise sauce, melt butter (do not brown). Leave to cool a little. Coarsely crush the peppercorns in a mortar. Peel and chop the shallot. Wash the herbs, shake dry and chop.
Bring vinegar, wine, shallot, peppercorns and half the herbs to the boil. Boil down to just under half the amount (= reduction). Pour through a sieve into a stainless steel bowl. Stir in 1 tbsp. cold water, then egg yolk.
Whisk over a hot water bath (60-70 °C) for a few minutes with a whisk until a thick cream is formed. Remove from water bath and continue beating for 30 seconds.
Stir the liquid butter first drop by drop, then in a thin stream with a whisk into the egg cream. Important: Butter and egg yolk must have approximately the same temperature, otherwise the sauce can curdle!
Season Chateaubriand with sea salt and steak pepper. Stir the rest of the herbs into the béarnaise sauce. Season to taste with lemon juice, salt and pepper. Serve immediately with the Chateaubriand. Carrot vegetables go well with it.