Remove the steak from the fridge two hours before cooking and season liberally with salt.
Preheat the barbecue to hot. Rub steak with a little olive oil.
Place the steak on the grill and cook. For a rare steak, allow about six to seven minutes on each side depending on thickness; add a couple of minutes each side for medium. If the outside starts to burn before the steak is fully cooked, reduce the heat of the grill and cook until done to your liking. If your steak is very thick, you could simply use a meat thermometer to achieve the “done-ness” you prefer: 50°C for rare, 58°C for medium-rare.
Put steak on a plate, cover with foil and rest for 10 minutes.
For the salsa, place bread and vinegar in a mortar. Allow the bread to soak for a few minutes, then add the tarragon, garlic and salt. Pound with a pestle until a rough paste forms, then slowly add the oil until it forms a saucy consistency. Check seasoning.
Cut the fillet and sirloin away from the centre bone. Carve against the grain into 1½cm pieces. On a warmed plate, place the bone in the centre and rearrange the meat back next to it. Serve at the table with a bowl of salsa.