Preheat the oven to 200°C / 400°F / Gas mark 6.
Put the steak on a plate and rub with 2 tablespoons of olive oil and a generous grind of black pepper and salt.
Leave to rest at room temperature for 10 minutes.
Use a heavy ovenproof pan and allow it to become very hot on the hob.
Add the marinated meat to the pan, with the oil and juices from the plate, the garlic cloves, thyme and bay leaf.
Fry the steak for 3 minutes on the first side until well browned, basting with the oil and herbs using a spoon as it cooks.
Carefully remove the off the oil, add another 2 tablespoons, then fry the second side of the steak in the same way.
Quickly brown around the edges, using tongs, then slide the pan into the oven and roast for 15 minutes, turning over halfway through.
Remove the steak from the pan and rest it on a rack over a roasting tin.
Tip the oil, herbs and garlic from the pan over the steak, then leave to sit for 15-20 minutes uncovered.
Put a medium pan of water on to boil.
Add the vinegar, basil stalks, bay leaf and spices into a small pan.
Boil down to roughly 3 tablespoons, then strain yet keeping the liquid.
Put the egg yolks into a large bowl, add 1 tablespoon of cold water and 1 tablespoon of the vinegar reduction then whisk briefly until light and foamy.
Put the bowl over, but not touching, the simmering water, then whisk to an airy foam.
Slowly add the butter, whisking all the time.
Prevent the sauce overheating by lifting the bowl on and off the pan, adding a splash more water if it starts to get too thick.
Just before serving, finely chop the basil and stir into the sauce with the lemon juice and some salt and pepper to taste.