For the clarified butter::
Put the butter in a small saucepan and melt it over a very gentle heat. As the butter melts, all the curds, whey and impurities will rise to the surface. Using a small ladle, skim these off and discard. There will be some milk underneath the butter.
Carefully pour the clarified butter into a bowl through a sieve lined with muslin to trap all the impurities. Stop pouring when you reach the milk. Put to one side until needed.
For the dish: :
Season the lamb fillet with salt and pepper and pan fry in a hot pan.
For the tomatoes, pan fry them with garlic and thyme and deglaze the pan with sherry vinegar.
Melt the butter in a saucepan, and then add the shallots, garlic, peppercorns and herbs. Cook over a moderate heat for a few minutes but do not allow the ingredients to colour.
Pour the white wine vinegar into a pan and boil until it has totally evaporated. Add the wine and again boil liquid until it has been reduced to a syrup. Take the pan off the heat, remove the herbs and discard.
Place a saucepan of water on the stove to boil. Put the egg yolks in a stainless steel bowl, add the cold water, and place the bowl over the saucepan, which should be just below boiling point. Whisk the yolks until they thicken and form soft peaks.
Gradually add the warm clarified butter, whisking rapidly all the time until the sauce becomes smooth. Add the wine and shallot reduction, and continue beating vigorously over the hot water. Season the sauce with a little salt and a pinch of cayenne pepper. Squeeze in the lemon juice. Serve.
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