Pre-heat the oven to 190°C
Start with the gastrique, the base for this sauce. Sweat a chopped shallot in a tbsp butter. Deglaze with 50 ml tarragon vinegar and 50 ml white wine.
Add 5 sprigs of tarragon, 5 crushed black peppercorns and a pinch of salt in a small saucepan over medium-high heat. Bring to a rapid simmer and cook till the liquid has reduced by about 75%.
Set aside to cool for a few minutes, then strain into a small bowl, pressing the shallot mixture with the back of a spoon to squeeze out all of the liquid. You should have about 2 tablespoons. If you're short, just add a little water to make up the difference.
Season 400g chateaubriand liberally on all sides with salt and pepper. Heat 1 tbsp butter and 1 tbsp olive oil in a heavy, ovenproof skillet over medium-high heat. Add the beef and sear until lightly browned on all sides, turning with tongs as needed, about 3 minutes total.
Place the skillet in the oven and roast for 10 to 12 minutes, until the oven thermometer registers 48° for medium rare. Wrap in foil and allow to rest for 10 minutes before carving (to avoid blood loss.)
In the meantime rinse and dry the saucepan and add 125g clarified butter. Melt completely over medium heat and keep warm.
Place 2 egg yolks and 2 tbsp gastrique into the bowl and whisk together until blended. Set the bowl over the simmering water and whisk vigorously as the eggs thicken and increase in volume, scraping the sides frequently to keep the mixture cooking evenly. You must whisk continually until the eggs have thickened to the point where you can see thin ribbons form when you lift the whisk. This should take about 5 minutes
To finish the sauce, whisk in the warm melted butter in a very slow drizzle. The sauce will thicken and develop a glossy sheen. Add 2 tbsp of hacked chervil and tarragon leaves each. Finish with some cayenne pepper.
Slice the meat, pour over the sauce and serve immediately.
Great with French fries.
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