Select a well-rounded onion. Peel outer skin off. Leave root intact and cut off any hanging roots. Using a small, sharp knife, divide onion into four sections by making 2 cuts crosswise, beginning at the top and cutting toward root, stopping about 1/2" away. Cut each section twice. Place onion in bowl of enough boiling water to cover it and leave for 5 minutes. The sections, or petals, will begin to open. Remove onion from water and immerse into ice water, which will further the opening. Drain well by turning upside down on paper towel. Put flour into paper bag, add onion and shake gently to coat with flour. Roll floured onion in beaten egg to cover. Put cracker crumbs or coating in bag, add onion, and shake gently to coat. Refrigerate 1 hour before deep frying in oil to golden brown, 3 to 5 minutes. Cooked onion can be kept for a time in warm oven.