The best way to preserve the delicate heads is to cook the asparagus with the head above the cooking water. The stems should be cut off to a level that leaves them all the same size. Some even peel the lower stems with a small sharp knife or vegetable peeler, and this is certainly necessary with older asparagus, especially the white asparagus, which usually has a thick woody skin. Remember to wash the tips in cold water to remove any grit before cooking.
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