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Prepare chimichurri sauce: Combine all chimichurri ingredients in the bowl of a food processor. Process 1 minute; season with salt and pepper. Chimichurri sauce may be stored in a covered container in the refrigerator for up to 1 week.
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Prepare steak: Pound skirt steak flat with a meat pounder. Transfer steaks to a shallow dish. Add 1 tablespoon oil, garlic, and parsley; turn steaks to coat. Marinate in refrigerator at least 2 hours and up to overnight.
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Preheat a grill pan. Brush grill pan with oil. Remove steaks from marinade, and season with salt and pepper. Place steaks on grill, and cook 2 to 3 minutes. Turn, and continue cooking to desired degree of doneness. Transfer steaks to a cutting board; let stand 10 minutes.
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Thinly slice steaks crosswise. Divide evenly between 4 plates and drizzle with chimichurri sauce. Serve with tomato wedges, onion, and watercress.