Pat steaks dry with paper towels and place on a rimmed baking sheet. Drizzle with olive oil and brush on both sides of the steak. Sprinkle with dry rub and set aside.
Prepare a grill fire to 350° using hickory or oak for smoke flavor. We are cooking on our large Big Green Egg with hickory chunks.
Add parsley, cilantro, garlic cloves, red wine vinegar, smoked paprika, salt, pepper and sugar to a blender or food processor. Pulse for 30 seconds until herbs are chopped.
With the blender running on low, slowly pour in the olive oil. Until well blended.
Pour chimichurri sauce into a serving bowl and set aside.
Place steaks over a hot grill fire and close the lid, cooking for 5 minutes.
Turn the steaks and continue to cook until desired doneness is reached. We pulled our steaks at 125°, using a digital meat thermometer.
Remove steaks from the grill and allow to rest 10 minutes before serving.
Slice steaks into thin strips and drizzle with chimichurri sauce.