In a blender, combine all ingredients except the pepper and oil. Pulse a few times, and then with the motor running, gradually add oil through the hole in the blender lid. Stop once or twice to scrape down sides so that all ingredients are incorporated. The vinaigrette will thicken.
Transfer to a bowl and season generously with pepper. Add more salt to taste, if needed. Use within an hour of preparation.
PREPARE THE STEAK:
In a 13x9-inch pyrex pan, stir together the oil, vinegar, garlic, oregano, cumin and ½ teaspoon pepper. Add the steak and let it marinate at room temperature, turning occasionally, for up to 2 hours.
Meanwhile, preheat the grill to high. When the grill is ready, lift the steak from the marinade (reserve marinade) and lay steak on the rack. Cover and grill, turning once and basting occasionally with marinade, until the steak is done to your liking, about 9 minutes for rare, which is recommended.
Transfer steak to cutting board and let it rest for 5 minutes.
FOR SERVING:
Carve the steak across the grain and at a slight angle to the cutting board into very thin slices. Season to taste with salt and pepper, and arrange steak slices on plates. Serve immediately, passing vinaigrette to drizzle on meat.