Brush steak with olive oil and season with salt and pepper.
Rub surface of grill pan with butter.
Place ribeye on hot grill pan with tongs, pressing down for great grill marks. Cook on one side 1 minute and 45 seconds, then rotate steak 90 degrees. After 2 minutes, flip steak and cook an additional 1 minute and 45 seconds. Rotate 90 degrees and finish cooking 2 minutes. Ensure steak is cooked until internal temperature reaches 145°F on meat thermometer for medium doneness before removing from grill.
Let steak rest 7-10 minutes.
Add all chimichurri ingredients into food processor and pulse until smooth.