Hawthorn, the original manufacturer of this style of cocktail strainer, now no longer exists, however name remains as a way of referring to this alien-looking device. The strainer should fit neatly over the top of a mixing glass or Boston tin. The small spring mechanism both enables a snug fit and prevents ice or pieces of fruit from coming through and spoiling your perfectly made cocktail. Incidentally, the coil from a Hawthorn shaker is removable, and when placed into a Boston tin with egg whites and shaken will provide a lovely, rich, thick mousse. Handy.
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Belvedere Vodka is a quality choice. Drinking responsibly is too.