Steak Béarnaise

Remove steaks from fridge, pat dry, set aside and cover with clingfilm. Peel  potatoes and cut into chips: cut slices about 1.5cm (¾in) thick, then chop  each into sticks the same width. Put into a bowl and cover with cold water for 30min. Drain and pat dry with kitchen paper – the chips need to be completely dry for crunchy results. 

Meanwhile, make Béarnaise: simmer the vinegar with 1tbsp water, the  peppercorns and tarragon stalks in a small pan until only 2tsp of liquid remains. Strain into a food processor with the yolks and pulse with a pinch of salt. Melt butter in the empty pan, being careful not to boil. Remove from heat and pour  into a jug. Switch on food processor and pour hot butter in a constant stream on to the yolks (as slowly as possible so the sauce thickens). Stir through  tarragon leaves and whiz again until smooth. Adjust taste with lemon juice and  more salt. Put sauce in a flask or a warm bowl covered in clingfilm sat in a larger bowl of tepid water for up to 1hr to keep warm and avoid it splitting. 

Reserve 1tbsp oil for the steaks. Pour remaining oil up to the mark inside a  deep fat fryer, or fill a large, deep saucepan half full with oil. Heat the oil up to  160°C. Carefully lift the basket out of the oil, add half the chips, and lower into the oil, or use a slotted metal spoon to lower half of the chips into the  saucepan. Fry for 6-7min, then raise frying basket or use a slotted metal spoon to scoop out chips on to kitchen roll to drain and cool. Repeat with remaining  chips. Turn off heat. 

In a wide non-stick frying pan over a high heat, add reserved 1tbsp oil. Pat  steaks dry with kitchen paper and season well, just before frying, with salt and pepper. When hot, add steaks to the pan, and fry for about 2min per side for rare, about 3min for medium or about 5min per side for well done, turning the temperature down after 3min. Hold the fatty edge down with tongs for 2min so that it renders. Remove from heat; rest steaks for 10min. 

To finish chips, increase oil heat to 190°C and fry all the chips together for  3min, until crisp and golden. Drain, sprinkle with salt and serve immediately. Serve steaks, chips and Béarnaise sauce with a simple side salad.