Remove steaks from the fridge 30 minutes before cooking, allowing them to warm to room temperature for even cooking and maximum tenderness*.
Heat one half of the grill to medium-high (about 450°F / 232°C), leaving the other side off.
Pat dry the steaks with paper towels to remove excess moisture. Then rub in the salt and ground pepper followed by the olive oil.
Preheat grill to medium-high or 450°F (232°C).
Place your palm about 3 inches above the grill grates. If you can only hold it for 1-2 seconds the grill is ready. (The grates should be hot enough before the steak goes on.)
Carefully grease the grates with oil using a folded paper towel, in order to prevent sticking.
Place the chuck eye steaks on the cool side of the grill for 25-30 minutes for medium-rare steak**.
Then move the steaks to the hot side and sear for 1-2 minutes PER SIDE, using tongs to flip. (Optional: to get crosshatch grill marks, rotate 90 degrees halfway through on each side.)
Insert an instant meat thermometer into the thickest part of the steak. Remove from the grill at 120°F (49°C) for rare, 130°F (54°C) for medium-rare, and 140°F (60°C) for medium. Note: The temperature will rise a few degrees more while resting.
Transfer the steak to a plate, covering with aluminum foil and let rest for 5-10 minutes. (This will allow the juices to retreat back into the meat before serving).
Garnish with optional butter and herbs. Slice against the grain to serve.