First make the chimichurri. Add all the ingredients to a food-processor and pulse until roughly chopped. Transfer to a bowl and set aside.
Prepare a charcoal barbecue or heat a gas barbecue to a high heat, or place a griddle pan over a high heat. Sprinkle the steak with salt and pepper and grill for 3 minutes on each side for medium-rare. Set aside and keep warm. Grill the chicory for 1 minute on each side or until golden. Remove from the barbecue or pan, then drizzle with oil and season with salt and pepper.
Thinly slice the steak, spoon over the chimichurri and serve with the grilled chicory.