To make the shallot and tarragon butter, heat the oil and a knob of the butter in a small pan. Add the shallots and gently fry for 6-8 minutes until softened but not coloured. Leave to cool, then beat in the peppercorns, mustard, tarragon, chives and the remaining butter. Spoon on to a sheet of parchment paper and shape into a roll about 4 cm thick. Chill until firm and use as required.
Remove the t-bone steaks from the fridge about 30 minutes before you want to cook them and rub the olive oil all over them. Season with salt and pepper just before cooking.
If using a charcoal barbecue, light it 30 minutes before you want to start cooking. If using a gas barbecue, light it 10 minutes beforehand. Alternatively, use a large griddle pan. If using a griddle pan, place over a high heat until very hot. Sear the steaks for 2 minutes on each side, then cook for another 3 minutes on each side for medium-rare or longer if you prefer your meat more well done.
Remove the steaks from the heat and place on warmed plates. Cut the shallot and tarragon butter into slices and put a couple on each steak. Leave to rest in a warm place for 5 minutes. Add the crispy potato wedges to each plate and serve with the green salad.