To make chimichurri, place all ingredients except lamb in a large bowl, season; stir to combine.
Place half the chimichurri in a large bowl with the lamb; toss to coat in the marinade. Cover; refrigerate 3 hours or overnight. Cover remaining chimichurri; refrigerate until required.
Preheat a grill pan (or barbecue) over high heat. Cook lamb, turning occasionally, for 4 minutes for medium or until cooked to your liking. Cover lamb; rest for 5 minutes.
Place lamb cutlets on a large platter; serve with reserved chimichurri. Sprinkle over extra fresh parsley sprigs to serve, if you like.