Leave the beef at room temperature for about 1 hr before you cook it. Heat oven to 60C/40C fan/gas 1 /4 if you like your beef medium rare, or 65C/45C fan/gas 1 /4 for medium. (Cooking at these low temperatures will be more accurate in an electric oven than in a gas one. If using gas, put the oven on the lowest setting you have, and be aware that the cooking time may be shorter.)
Put the unseasoned beef in a heavy-based ovenproof frying pan. Cook in the middle of the oven for 3 hrs undisturbed.
Meanwhile, make the salsa. Zest the limes and orange into a bowl. Cut each in half and place, cut-side down, in a hot pan. Cook for a few mins until the fruits are charred, then squeeze the juice into the bowl. Add the other ingredients and season well.
When the beef is cooked, it should look dry on the surface, and dark pink in colour. If you have a meat thermometer, test the internal temperature – it should be 58-60C. Remove the pan from the oven and set over a high heat on the hob. Add the oil and sear the meat on both sides for a few mins until caramelised. Sear the fat for a few mins too. Smash the garlic clove with the heel of your hand and add this to the pan with the thyme and butter. When the butter is foaming, spoon it over the beef and cook for another 1-2 mins. Transfer the beef to a warm plate, cover with foil, and leave to rest for 5-10 mins. Carve away from the bone and into slices before serving with the salsa, fries and salad.