Gently warm the barbecue and wait until it gets really hot. Brush the rib eye steaks all over with the oil, then season them with salt and black pepper.
Grill the steaks over a high heat for 1½ minutes on each side, then remove them and place to one side for 15 minutes. After quarter of an hour, put the steaks back on the hot grill, cover them and leave them to cook for 4 to 6 minutes. The steaks are done once the thermometer shows 54 °C to 57 °C for very rare / rare in the middle. If you like your steak medium done, wait until it reaches 60 °C.
Remove the rib eye steaks and place on a chopping board. Leave them to rest for 10 minutes. Carve and serve.
If you are using a plancha grill:
At the start, sear the meat over a high temperature.
Then leave the meat to cook at as low a temperature as possible until it is cooked just how you want it.