Mix together first six ingredients to make chimichurri and set aside for at least one hour.
Light charcoal 30 minutes in advance to build a good coal bed.
Place steak on a rack and season generously with salt on both sides. Move steak to grill over medium-high heat and leave untouched on first side for 3 minutes.
Flip steak and cook on second side for 3-4 minutes, adjusting coals if heat seems too hot.
Season steak with pepper as it is coming off the grill.
Place steak in baking dish or other container and pour chimichurri over the top; allow to rest, uncovered for at least 10 minutes, flipping halfway through. Reserve excess chimichurri for garnish.
Place chimichurri-marinated steak back on the grill to reheat over medium-high heat for no more than one minute per side.
Slice steak against the grain (going with the grain results in a steak that is tough).
Place on a platter and spoon some of the extra chimichurri on top.