Combine sauce ingredients in a blender or food processor, blend until smooth. Taste and adjust seasonings as desired. Pour into small serving bowl and set aside.
Brush steaks with olive oil and sprinkle with salt and pepper.
Brush grates of a clean gas grill (or cast iron grill on stove top) with olive oil and heat to medium.
Cook steaks over medium heat for 2-3 minutes, lift steak and rotate ¼ turn (do not flip) and cook another 1-2 minutes.
Flip and cook for 2-3 minutes, then lift and rotate steak ¼ turn to create those lovely cross marks.
Continue cooking for another few minutes, depending on how well you like the steaks done. Check the internal temperature with an instant-read thermometer a minute or two after the final rotation to determine final cooking time. (see chart above)
Remove from heat, tent with a piece of aluminum foil and allow the steaks to rest for 10 minutes before slicing and serving with green sauce on the side.
Notes
For best results, remove the steak from the refrigerator at least 30 minutes prior to grilling.