For the sauce, cook a reduction (boil down liquid to concentrate the flavours): For this, peel and dice the shallot. Wash the tarragon. Boil up wine, vinegar, shallot, peppercorns and 3 stems of tarragon.
Boil until the liquid is reduced to approx. 1⁄3 (3-4 tablespoons). Pour through a fine sieve. Allow to cool.
Peel and wash the potatoes and slice them into thin slices. Heat the oil in a deep fryer or a high pot to approx. 180 °C. Fry the potatoes in it in portions until golden brown. Drain on kitchen paper.
Season with salt and keep warm.
Dab steaks dry, fry in hot lard on each side for 3-5 minutes. Season with salt and pepper. Let it rest in aluminium foil for about 10 minutes.
Melt the butter. Whisk the egg yolk and the reduction in a hot water bath until thick and creamy. Add warm liquid butter, first drop by drop, then in a thin stream, stirring constantly.
If the sauce becomes too firm or curdles, add ice cold water drop by drop. Chop the rest of the tarragon and stir in. Season sauce with salt, pepper and lemon juice. Serve everything. Serve with fried cherry tomatoes.