Mix the thyme, lemon rind, 2 tablespoons of the oil and some salt and pepper together and rub it all over the beef fillet. Wrap the prosciutto around the beef to flavour it and keep it moist, and secure in place with cooking string.
Cook on the flat plate of a hot gas barbecue for 25 minutes, turning frequently (or use the indirect grilling method for a charcoal barbecue). Remove the beef, wrap in a double layer of foil and set aside to rest for 20 minutes.
Meanwhile, cut the potatoes lengthways into 1 cm (½ inch) thick slices and parboil for 5 minutes. Drain well, brush with the remaining oil and season with salt and pepper. Cook the potato slices on the grill rack for 3—4 minutes on each side until charred and tender.
Slice the beef and serve with the potatoes and a spinach salad (see below).