Scrape the scales from the fish, cut off the fins and remove the eyes, but leave the head and tail on. Gut the fish if necessary and keep the liver. Wash well. Season the inside of each fish and replace the liver. Brush the fish with olive oil and put a little oil in the grill-pan before putting in the fish. Grill quickly for 3 min., then turn the fish over and baste well. Reduce the heat and continue grilling until the mullet are cooked, about a further 15 min. Serve on a hot dish with the remaining oil poured over. Garnish with parsley.