In a blender or small food processor, combine cilantro, green onion, vinegar, garlic, salt, cayenne pepper and black pepper. Cover and blend or process for 30 seconds. With the blender or processor running, add the oil in a thin, steady stream; blend or process until combined. Let stand, covered, in blender or food processor for 20 minutes to blend flavors.
If using steaks, trim fat from steaks. For a charcoal grill, grill steaks on the rack of an uncovered grill directly over medium coals to desired doneness, turning once halfway through grilling. For ribeye steaks, allow 11 to 15 minutes for medium-rare (145 degrees F) and 14 to 18 minutes for medium (160 degrees F). For sirloin steak, allow 14 to 18 minutes for medium-rare (145 degrees F) and 18 to 22 minutes for medium (160 degrees F). (For a gas grill, preheat grill on high heat. Reduce heat to medium. Cover and grill as above.) if using shrimp, grill shrimp for 3 minutes on each side or until shrimp are opaque.
If using steaks, cut steaks into 6 serving-size pieces. Blend or process chimichurri for 10 seconds. Pour a little chimichurri onto a warmed serving platter. Place steaks or shrimp on top of chimichurri and drizzle remaining chimichurri over. Serve immediately.